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## Research Questions & Hypotheses

Generally, in quantitative studies, reviewers expect hypotheses rather than research questions. However, both research questions and hypotheses serve different purposes and can be beneficial when used together.

## Research Questions

Clarify the research’s aim (farrugia et al., 2010).

- Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
- Descriptive: “What factors most influence the academic achievement of senior high school students?”
- Comparative: “What is the performance difference between teaching methods A and B?”
- Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
- Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
- Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
- The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
- It’s advisable to focus on a single primary research question for the study.
- The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
- The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.
- The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.
- Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
- The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
- A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
- A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
- An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

## Checklist: Good research questions for social science projects (Panke, 2018)

## Research Hypotheses

Present the researcher’s predictions based on specific statements.

- These statements define the research problem or issue and indicate the direction of the researcher’s predictions.
- Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.
- The research or clinical hypothesis, derived from the research question, shapes the study’s key elements: sampling strategy, intervention, comparison, and outcome variables.
- Hypotheses can express a single outcome or multiple outcomes.
- After statistical testing, the null hypothesis is either rejected or not rejected based on whether the study’s findings are statistically significant.
- Hypothesis testing helps determine if observed findings are due to true differences and not chance.
- Hypotheses can be 1-sided (specific direction of difference) or 2-sided (presence of a difference without specifying direction).
- 2-sided hypotheses are generally preferred unless there’s a strong justification for a 1-sided hypothesis.
- A solid research hypothesis, informed by a good research question, influences the research design and paves the way for defining clear research objectives.

## Types of Research Hypothesis

- In a Y-centered research design, the focus is on the dependent variable (DV) which is specified in the research question. Theories are then used to identify independent variables (IV) and explain their causal relationship with the DV.
- Example: “An increase in teacher-led instructional time (IV) is likely to improve student reading comprehension scores (DV), because extensive guided practice under expert supervision enhances learning retention and skill mastery.”
- Hypothesis Explanation: The dependent variable (student reading comprehension scores) is the focus, and the hypothesis explores how changes in the independent variable (teacher-led instructional time) affect it.
- In X-centered research designs, the independent variable is specified in the research question. Theories are used to determine potential dependent variables and the causal mechanisms at play.
- Example: “Implementing technology-based learning tools (IV) is likely to enhance student engagement in the classroom (DV), because interactive and multimedia content increases student interest and participation.”
- Hypothesis Explanation: The independent variable (technology-based learning tools) is the focus, with the hypothesis exploring its impact on a potential dependent variable (student engagement).
- Probabilistic hypotheses suggest that changes in the independent variable are likely to lead to changes in the dependent variable in a predictable manner, but not with absolute certainty.
- Example: “The more teachers engage in professional development programs (IV), the more their teaching effectiveness (DV) is likely to improve, because continuous training updates pedagogical skills and knowledge.”
- Hypothesis Explanation: This hypothesis implies a probable relationship between the extent of professional development (IV) and teaching effectiveness (DV).
- Deterministic hypotheses state that a specific change in the independent variable will lead to a specific change in the dependent variable, implying a more direct and certain relationship.
- Example: “If the school curriculum changes from traditional lecture-based methods to project-based learning (IV), then student collaboration skills (DV) are expected to improve because project-based learning inherently requires teamwork and peer interaction.”
- Hypothesis Explanation: This hypothesis presumes a direct and definite outcome (improvement in collaboration skills) resulting from a specific change in the teaching method.
- Example : “Students who identify as visual learners will score higher on tests that are presented in a visually rich format compared to tests presented in a text-only format.”
- Explanation : This hypothesis aims to describe the potential difference in test scores between visual learners taking visually rich tests and text-only tests, without implying a direct cause-and-effect relationship.
- Example : “Teaching method A will improve student performance more than method B.”
- Explanation : This hypothesis compares the effectiveness of two different teaching methods, suggesting that one will lead to better student performance than the other. It implies a direct comparison but does not necessarily establish a causal mechanism.
- Example : “Students with higher self-efficacy will show higher levels of academic achievement.”
- Explanation : This hypothesis predicts a relationship between the variable of self-efficacy and academic achievement. Unlike a causal hypothesis, it does not necessarily suggest that one variable causes changes in the other, but rather that they are related in some way.

## Tips for developing research questions and hypotheses for research studies

- Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
- Learn about current trends and technological advances on the topic.
- Seek careful input from experts, mentors, colleagues, and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
- Use the FINER criteria in the development of the research question.
- Ensure that the research question follows PICOT format.
- Develop a research hypothesis from the research question.
- Ensure that the research question and objectives are answerable, feasible, and clinically relevant.

If your research hypotheses are derived from your research questions, particularly when multiple hypotheses address a single question, it’s recommended to use both research questions and hypotheses. However, if this isn’t the case, using hypotheses over research questions is advised. It’s important to note these are general guidelines, not strict rules. If you opt not to use hypotheses, consult with your supervisor for the best approach.

Farrugia, P., Petrisor, B. A., Farrokhyar, F., & Bhandari, M. (2010). Practical tips for surgical research: Research questions, hypotheses and objectives. Canadian journal of surgery. Journal canadien de chirurgie , 53 (4), 278–281.

Hulley, S. B., Cummings, S. R., Browner, W. S., Grady, D., & Newman, T. B. (2007). Designing clinical research. Philadelphia.

Panke, D. (2018). Research design & method selection: Making good choices in the social sciences. Research Design & Method Selection , 1-368.

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- How to Write a Strong Hypothesis | Guide & Examples

## How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

## Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

## Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

## Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

## Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

## Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

## Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

- The relevant variables
- The specific group being studied
- The predicted outcome of the experiment or analysis

## Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

## Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

## Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 14 May 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

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## How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk, "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

- The Scientific Method

## Hypothesis Format

Falsifiability of a hypothesis.

- Operationalization

## Hypothesis Types

Hypotheses examples.

- Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

## At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

## The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

- Forming a question
- Performing background research
- Creating a hypothesis
- Designing an experiment
- Collecting data
- Analyzing the results
- Drawing conclusions
- Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

## Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

- Is your hypothesis based on your research on a topic?
- Can your hypothesis be tested?
- Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the journal articles you read . Many authors will suggest questions that still need to be explored.

## How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

- Collect as many observations about a topic or problem as you can.
- Evaluate these observations and look for possible causes of the problem.
- Create a list of possible explanations that you might want to explore.
- After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method , falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that if something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

## The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

## Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

## Hypothesis Checklist

- Does your hypothesis focus on something that you can actually test?
- Does your hypothesis include both an independent and dependent variable?
- Can you manipulate the variables?
- Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

- Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
- Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
- Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
- Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
- Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
- Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

## A few examples of simple hypotheses:

- "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
- "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."
- "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
- "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

## Examples of a complex hypothesis include:

- "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
- "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

## Examples of a null hypothesis include:

- "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
- "There is no difference in scores on a memory recall task between children and adults."
- "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

## Examples of an alternative hypothesis:

- "People who take St. John's wort supplements will have less anxiety than those who do not."
- "Adults will perform better on a memory task than children."
- "Children who play first-person shooter games will show higher levels of aggression than children who do not."

## Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

## Descriptive Research Methods

Descriptive research such as case studies , naturalistic observations , and surveys are often used when conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

## Experimental Research Methods

Experimental methods are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually cause another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses . R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:]. Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ? PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies . Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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## Research questions, hypotheses and objectives

Patricia farrugia.

* Michael G. DeGroote School of Medicine, the

## Bradley A. Petrisor

† Division of Orthopaedic Surgery and the

## Forough Farrokhyar

‡ Departments of Surgery and

§ Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Ont

## Mohit Bhandari

There is an increasing familiarity with the principles of evidence-based medicine in the surgical community. As surgeons become more aware of the hierarchy of evidence, grades of recommendations and the principles of critical appraisal, they develop an increasing familiarity with research design. Surgeons and clinicians are looking more and more to the literature and clinical trials to guide their practice; as such, it is becoming a responsibility of the clinical research community to attempt to answer questions that are not only well thought out but also clinically relevant. The development of the research question, including a supportive hypothesis and objectives, is a necessary key step in producing clinically relevant results to be used in evidence-based practice. A well-defined and specific research question is more likely to help guide us in making decisions about study design and population and subsequently what data will be collected and analyzed. 1

## Objectives of this article

In this article, we discuss important considerations in the development of a research question and hypothesis and in defining objectives for research. By the end of this article, the reader will be able to appreciate the significance of constructing a good research question and developing hypotheses and research objectives for the successful design of a research study. The following article is divided into 3 sections: research question, research hypothesis and research objectives.

## Research question

Interest in a particular topic usually begins the research process, but it is the familiarity with the subject that helps define an appropriate research question for a study. 1 Questions then arise out of a perceived knowledge deficit within a subject area or field of study. 2 Indeed, Haynes suggests that it is important to know “where the boundary between current knowledge and ignorance lies.” 1 The challenge in developing an appropriate research question is in determining which clinical uncertainties could or should be studied and also rationalizing the need for their investigation.

Increasing one’s knowledge about the subject of interest can be accomplished in many ways. Appropriate methods include systematically searching the literature, in-depth interviews and focus groups with patients (and proxies) and interviews with experts in the field. In addition, awareness of current trends and technological advances can assist with the development of research questions. 2 It is imperative to understand what has been studied about a topic to date in order to further the knowledge that has been previously gathered on a topic. Indeed, some granting institutions (e.g., Canadian Institute for Health Research) encourage applicants to conduct a systematic review of the available evidence if a recent review does not already exist and preferably a pilot or feasibility study before applying for a grant for a full trial.

In-depth knowledge about a subject may generate a number of questions. It then becomes necessary to ask whether these questions can be answered through one study or if more than one study needed. 1 Additional research questions can be developed, but several basic principles should be taken into consideration. 1 All questions, primary and secondary, should be developed at the beginning and planning stages of a study. Any additional questions should never compromise the primary question because it is the primary research question that forms the basis of the hypothesis and study objectives. It must be kept in mind that within the scope of one study, the presence of a number of research questions will affect and potentially increase the complexity of both the study design and subsequent statistical analyses, not to mention the actual feasibility of answering every question. 1 A sensible strategy is to establish a single primary research question around which to focus the study plan. 3 In a study, the primary research question should be clearly stated at the end of the introduction of the grant proposal, and it usually specifies the population to be studied, the intervention to be implemented and other circumstantial factors. 4

Hulley and colleagues 2 have suggested the use of the FINER criteria in the development of a good research question ( Box 1 ). The FINER criteria highlight useful points that may increase the chances of developing a successful research project. A good research question should specify the population of interest, be of interest to the scientific community and potentially to the public, have clinical relevance and further current knowledge in the field (and of course be compliant with the standards of ethical boards and national research standards).

## FINER criteria for a good research question

Adapted with permission from Wolters Kluwer Health. 2

Whereas the FINER criteria outline the important aspects of the question in general, a useful format to use in the development of a specific research question is the PICO format — consider the population (P) of interest, the intervention (I) being studied, the comparison (C) group (or to what is the intervention being compared) and the outcome of interest (O). 3 , 5 , 6 Often timing (T) is added to PICO ( Box 2 ) — that is, “Over what time frame will the study take place?” 1 The PICOT approach helps generate a question that aids in constructing the framework of the study and subsequently in protocol development by alluding to the inclusion and exclusion criteria and identifying the groups of patients to be included. Knowing the specific population of interest, intervention (and comparator) and outcome of interest may also help the researcher identify an appropriate outcome measurement tool. 7 The more defined the population of interest, and thus the more stringent the inclusion and exclusion criteria, the greater the effect on the interpretation and subsequent applicability and generalizability of the research findings. 1 , 2 A restricted study population (and exclusion criteria) may limit bias and increase the internal validity of the study; however, this approach will limit external validity of the study and, thus, the generalizability of the findings to the practical clinical setting. Conversely, a broadly defined study population and inclusion criteria may be representative of practical clinical practice but may increase bias and reduce the internal validity of the study.

## PICOT criteria 1

A poorly devised research question may affect the choice of study design, potentially lead to futile situations and, thus, hamper the chance of determining anything of clinical significance, which will then affect the potential for publication. Without devoting appropriate resources to developing the research question, the quality of the study and subsequent results may be compromised. During the initial stages of any research study, it is therefore imperative to formulate a research question that is both clinically relevant and answerable.

## Research hypothesis

The primary research question should be driven by the hypothesis rather than the data. 1 , 2 That is, the research question and hypothesis should be developed before the start of the study. This sounds intuitive; however, if we take, for example, a database of information, it is potentially possible to perform multiple statistical comparisons of groups within the database to find a statistically significant association. This could then lead one to work backward from the data and develop the “question.” This is counterintuitive to the process because the question is asked specifically to then find the answer, thus collecting data along the way (i.e., in a prospective manner). Multiple statistical testing of associations from data previously collected could potentially lead to spuriously positive findings of association through chance alone. 2 Therefore, a good hypothesis must be based on a good research question at the start of a trial and, indeed, drive data collection for the study.

The research or clinical hypothesis is developed from the research question and then the main elements of the study — sampling strategy, intervention (if applicable), comparison and outcome variables — are summarized in a form that establishes the basis for testing, statistical and ultimately clinical significance. 3 For example, in a research study comparing computer-assisted acetabular component insertion versus freehand acetabular component placement in patients in need of total hip arthroplasty, the experimental group would be computer-assisted insertion and the control/conventional group would be free-hand placement. The investigative team would first state a research hypothesis. This could be expressed as a single outcome (e.g., computer-assisted acetabular component placement leads to improved functional outcome) or potentially as a complex/composite outcome; that is, more than one outcome (e.g., computer-assisted acetabular component placement leads to both improved radiographic cup placement and improved functional outcome).

However, when formally testing statistical significance, the hypothesis should be stated as a “null” hypothesis. 2 The purpose of hypothesis testing is to make an inference about the population of interest on the basis of a random sample taken from that population. The null hypothesis for the preceding research hypothesis then would be that there is no difference in mean functional outcome between the computer-assisted insertion and free-hand placement techniques. After forming the null hypothesis, the researchers would form an alternate hypothesis stating the nature of the difference, if it should appear. The alternate hypothesis would be that there is a difference in mean functional outcome between these techniques. At the end of the study, the null hypothesis is then tested statistically. If the findings of the study are not statistically significant (i.e., there is no difference in functional outcome between the groups in a statistical sense), we cannot reject the null hypothesis, whereas if the findings were significant, we can reject the null hypothesis and accept the alternate hypothesis (i.e., there is a difference in mean functional outcome between the study groups), errors in testing notwithstanding. In other words, hypothesis testing confirms or refutes the statement that the observed findings did not occur by chance alone but rather occurred because there was a true difference in outcomes between these surgical procedures. The concept of statistical hypothesis testing is complex, and the details are beyond the scope of this article.

Another important concept inherent in hypothesis testing is whether the hypotheses will be 1-sided or 2-sided. A 2-sided hypothesis states that there is a difference between the experimental group and the control group, but it does not specify in advance the expected direction of the difference. For example, we asked whether there is there an improvement in outcomes with computer-assisted surgery or whether the outcomes worse with computer-assisted surgery. We presented a 2-sided test in the above example because we did not specify the direction of the difference. A 1-sided hypothesis states a specific direction (e.g., there is an improvement in outcomes with computer-assisted surgery). A 2-sided hypothesis should be used unless there is a good justification for using a 1-sided hypothesis. As Bland and Atlman 8 stated, “One-sided hypothesis testing should never be used as a device to make a conventionally nonsignificant difference significant.”

The research hypothesis should be stated at the beginning of the study to guide the objectives for research. Whereas the investigators may state the hypothesis as being 1-sided (there is an improvement with treatment), the study and investigators must adhere to the concept of clinical equipoise. According to this principle, a clinical (or surgical) trial is ethical only if the expert community is uncertain about the relative therapeutic merits of the experimental and control groups being evaluated. 9 It means there must exist an honest and professional disagreement among expert clinicians about the preferred treatment. 9

Designing a research hypothesis is supported by a good research question and will influence the type of research design for the study. Acting on the principles of appropriate hypothesis development, the study can then confidently proceed to the development of the research objective.

## Research objective

The primary objective should be coupled with the hypothesis of the study. Study objectives define the specific aims of the study and should be clearly stated in the introduction of the research protocol. 7 From our previous example and using the investigative hypothesis that there is a difference in functional outcomes between computer-assisted acetabular component placement and free-hand placement, the primary objective can be stated as follows: this study will compare the functional outcomes of computer-assisted acetabular component insertion versus free-hand placement in patients undergoing total hip arthroplasty. Note that the study objective is an active statement about how the study is going to answer the specific research question. Objectives can (and often do) state exactly which outcome measures are going to be used within their statements. They are important because they not only help guide the development of the protocol and design of study but also play a role in sample size calculations and determining the power of the study. 7 These concepts will be discussed in other articles in this series.

From the surgeon’s point of view, it is important for the study objectives to be focused on outcomes that are important to patients and clinically relevant. For example, the most methodologically sound randomized controlled trial comparing 2 techniques of distal radial fixation would have little or no clinical impact if the primary objective was to determine the effect of treatment A as compared to treatment B on intraoperative fluoroscopy time. However, if the objective was to determine the effect of treatment A as compared to treatment B on patient functional outcome at 1 year, this would have a much more significant impact on clinical decision-making. Second, more meaningful surgeon–patient discussions could ensue, incorporating patient values and preferences with the results from this study. 6 , 7 It is the precise objective and what the investigator is trying to measure that is of clinical relevance in the practical setting.

The following is an example from the literature about the relation between the research question, hypothesis and study objectives:

Study: Warden SJ, Metcalf BR, Kiss ZS, et al. Low-intensity pulsed ultrasound for chronic patellar tendinopathy: a randomized, double-blind, placebo-controlled trial. Rheumatology 2008;47:467–71.

Research question: How does low-intensity pulsed ultrasound (LIPUS) compare with a placebo device in managing the symptoms of skeletally mature patients with patellar tendinopathy?

Research hypothesis: Pain levels are reduced in patients who receive daily active-LIPUS (treatment) for 12 weeks compared with individuals who receive inactive-LIPUS (placebo).

Objective: To investigate the clinical efficacy of LIPUS in the management of patellar tendinopathy symptoms.

The development of the research question is the most important aspect of a research project. A research project can fail if the objectives and hypothesis are poorly focused and underdeveloped. Useful tips for surgical researchers are provided in Box 3 . Designing and developing an appropriate and relevant research question, hypothesis and objectives can be a difficult task. The critical appraisal of the research question used in a study is vital to the application of the findings to clinical practice. Focusing resources, time and dedication to these 3 very important tasks will help to guide a successful research project, influence interpretation of the results and affect future publication efforts.

## Tips for developing research questions, hypotheses and objectives for research studies

- Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
- Learn about current trends and technological advances on the topic.
- Seek careful input from experts, mentors, colleagues and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
- Use the FINER criteria in the development of the research question.
- Ensure that the research question follows PICOT format.
- Develop a research hypothesis from the research question.
- Develop clear and well-defined primary and secondary (if needed) objectives.
- Ensure that the research question and objectives are answerable, feasible and clinically relevant.

FINER = feasible, interesting, novel, ethical, relevant; PICOT = population (patients), intervention (for intervention studies only), comparison group, outcome of interest, time.

Competing interests: No funding was received in preparation of this paper. Dr. Bhandari was funded, in part, by a Canada Research Chair, McMaster University.

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## What is and How to Write a Good Hypothesis in Research?

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One of the most important aspects of conducting research is constructing a strong hypothesis. But what makes a hypothesis in research effective? In this article, we’ll look at the difference between a hypothesis and a research question, as well as the elements of a good hypothesis in research. We’ll also include some examples of effective hypotheses, and what pitfalls to avoid.

## What is a Hypothesis in Research?

Simply put, a hypothesis is a research question that also includes the predicted or expected result of the research. Without a hypothesis, there can be no basis for a scientific or research experiment. As such, it is critical that you carefully construct your hypothesis by being deliberate and thorough, even before you set pen to paper. Unless your hypothesis is clearly and carefully constructed, any flaw can have an adverse, and even grave, effect on the quality of your experiment and its subsequent results.

## Research Question vs Hypothesis

It’s easy to confuse research questions with hypotheses, and vice versa. While they’re both critical to the Scientific Method, they have very specific differences. Primarily, a research question, just like a hypothesis, is focused and concise. But a hypothesis includes a prediction based on the proposed research, and is designed to forecast the relationship of and between two (or more) variables. Research questions are open-ended, and invite debate and discussion, while hypotheses are closed, e.g. “The relationship between A and B will be C.”

A hypothesis is generally used if your research topic is fairly well established, and you are relatively certain about the relationship between the variables that will be presented in your research. Since a hypothesis is ideally suited for experimental studies, it will, by its very existence, affect the design of your experiment. The research question is typically used for new topics that have not yet been researched extensively. Here, the relationship between different variables is less known. There is no prediction made, but there may be variables explored. The research question can be casual in nature, simply trying to understand if a relationship even exists, descriptive or comparative.

## How to Write Hypothesis in Research

Writing an effective hypothesis starts before you even begin to type. Like any task, preparation is key, so you start first by conducting research yourself, and reading all you can about the topic that you plan to research. From there, you’ll gain the knowledge you need to understand where your focus within the topic will lie.

Remember that a hypothesis is a prediction of the relationship that exists between two or more variables. Your job is to write a hypothesis, and design the research, to “prove” whether or not your prediction is correct. A common pitfall is to use judgments that are subjective and inappropriate for the construction of a hypothesis. It’s important to keep the focus and language of your hypothesis objective.

An effective hypothesis in research is clearly and concisely written, and any terms or definitions clarified and defined. Specific language must also be used to avoid any generalities or assumptions.

Use the following points as a checklist to evaluate the effectiveness of your research hypothesis:

- Predicts the relationship and outcome
- Simple and concise – avoid wordiness
- Clear with no ambiguity or assumptions about the readers’ knowledge
- Observable and testable results
- Relevant and specific to the research question or problem

## Research Hypothesis Example

Perhaps the best way to evaluate whether or not your hypothesis is effective is to compare it to those of your colleagues in the field. There is no need to reinvent the wheel when it comes to writing a powerful research hypothesis. As you’re reading and preparing your hypothesis, you’ll also read other hypotheses. These can help guide you on what works, and what doesn’t, when it comes to writing a strong research hypothesis.

Here are a few generic examples to get you started.

Eating an apple each day, after the age of 60, will result in a reduction of frequency of physician visits.

Budget airlines are more likely to receive more customer complaints. A budget airline is defined as an airline that offers lower fares and fewer amenities than a traditional full-service airline. (Note that the term “budget airline” is included in the hypothesis.

Workplaces that offer flexible working hours report higher levels of employee job satisfaction than workplaces with fixed hours.

Each of the above examples are specific, observable and measurable, and the statement of prediction can be verified or shown to be false by utilizing standard experimental practices. It should be noted, however, that often your hypothesis will change as your research progresses.

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## How to Write a Research Hypothesis: Good & Bad Examples

## What is a research hypothesis?

A research hypothesis is an attempt at explaining a phenomenon or the relationships between phenomena/variables in the real world. Hypotheses are sometimes called “educated guesses”, but they are in fact (or let’s say they should be) based on previous observations, existing theories, scientific evidence, and logic. A research hypothesis is also not a prediction—rather, predictions are ( should be) based on clearly formulated hypotheses. For example, “We tested the hypothesis that KLF2 knockout mice would show deficiencies in heart development” is an assumption or prediction, not a hypothesis.

The research hypothesis at the basis of this prediction is “the product of the KLF2 gene is involved in the development of the cardiovascular system in mice”—and this hypothesis is probably (hopefully) based on a clear observation, such as that mice with low levels of Kruppel-like factor 2 (which KLF2 codes for) seem to have heart problems. From this hypothesis, you can derive the idea that a mouse in which this particular gene does not function cannot develop a normal cardiovascular system, and then make the prediction that we started with.

## What is the difference between a hypothesis and a prediction?

You might think that these are very subtle differences, and you will certainly come across many publications that do not contain an actual hypothesis or do not make these distinctions correctly. But considering that the formulation and testing of hypotheses is an integral part of the scientific method, it is good to be aware of the concepts underlying this approach. The two hallmarks of a scientific hypothesis are falsifiability (an evaluation standard that was introduced by the philosopher of science Karl Popper in 1934) and testability —if you cannot use experiments or data to decide whether an idea is true or false, then it is not a hypothesis (or at least a very bad one).

So, in a nutshell, you (1) look at existing evidence/theories, (2) come up with a hypothesis, (3) make a prediction that allows you to (4) design an experiment or data analysis to test it, and (5) come to a conclusion. Of course, not all studies have hypotheses (there is also exploratory or hypothesis-generating research), and you do not necessarily have to state your hypothesis as such in your paper.

But for the sake of understanding the principles of the scientific method, let’s first take a closer look at the different types of hypotheses that research articles refer to and then give you a step-by-step guide for how to formulate a strong hypothesis for your own paper.

## Types of Research Hypotheses

Hypotheses can be simple , which means they describe the relationship between one single independent variable (the one you observe variations in or plan to manipulate) and one single dependent variable (the one you expect to be affected by the variations/manipulation). If there are more variables on either side, you are dealing with a complex hypothesis. You can also distinguish hypotheses according to the kind of relationship between the variables you are interested in (e.g., causal or associative ). But apart from these variations, we are usually interested in what is called the “alternative hypothesis” and, in contrast to that, the “null hypothesis”. If you think these two should be listed the other way round, then you are right, logically speaking—the alternative should surely come second. However, since this is the hypothesis we (as researchers) are usually interested in, let’s start from there.

## Alternative Hypothesis

If you predict a relationship between two variables in your study, then the research hypothesis that you formulate to describe that relationship is your alternative hypothesis (usually H1 in statistical terms). The goal of your hypothesis testing is thus to demonstrate that there is sufficient evidence that supports the alternative hypothesis, rather than evidence for the possibility that there is no such relationship. The alternative hypothesis is usually the research hypothesis of a study and is based on the literature, previous observations, and widely known theories.

## Null Hypothesis

The hypothesis that describes the other possible outcome, that is, that your variables are not related, is the null hypothesis ( H0 ). Based on your findings, you choose between the two hypotheses—usually that means that if your prediction was correct, you reject the null hypothesis and accept the alternative. Make sure, however, that you are not getting lost at this step of the thinking process: If your prediction is that there will be no difference or change, then you are trying to find support for the null hypothesis and reject H1.

## Directional Hypothesis

While the null hypothesis is obviously “static”, the alternative hypothesis can specify a direction for the observed relationship between variables—for example, that mice with higher expression levels of a certain protein are more active than those with lower levels. This is then called a one-tailed hypothesis.

Another example for a directional one-tailed alternative hypothesis would be that

H1: Attending private classes before important exams has a positive effect on performance.

Your null hypothesis would then be that

H0: Attending private classes before important exams has no/a negative effect on performance.

## Nondirectional Hypothesis

A nondirectional hypothesis does not specify the direction of the potentially observed effect, only that there is a relationship between the studied variables—this is called a two-tailed hypothesis. For instance, if you are studying a new drug that has shown some effects on pathways involved in a certain condition (e.g., anxiety) in vitro in the lab, but you can’t say for sure whether it will have the same effects in an animal model or maybe induce other/side effects that you can’t predict and potentially increase anxiety levels instead, you could state the two hypotheses like this:

H1: The only lab-tested drug (somehow) affects anxiety levels in an anxiety mouse model.

You then test this nondirectional alternative hypothesis against the null hypothesis:

H0: The only lab-tested drug has no effect on anxiety levels in an anxiety mouse model.

## How to Write a Hypothesis for a Research Paper

Now that we understand the important distinctions between different kinds of research hypotheses, let’s look at a simple process of how to write a hypothesis.

## Writing a Hypothesis Step:1

Ask a question, based on earlier research. Research always starts with a question, but one that takes into account what is already known about a topic or phenomenon. For example, if you are interested in whether people who have pets are happier than those who don’t, do a literature search and find out what has already been demonstrated. You will probably realize that yes, there is quite a bit of research that shows a relationship between happiness and owning a pet—and even studies that show that owning a dog is more beneficial than owning a cat ! Let’s say you are so intrigued by this finding that you wonder:

What is it that makes dog owners even happier than cat owners?

Let’s move on to Step 2 and find an answer to that question.

## Writing a Hypothesis Step 2:

Formulate a strong hypothesis by answering your own question. Again, you don’t want to make things up, take unicorns into account, or repeat/ignore what has already been done. Looking at the dog-vs-cat papers your literature search returned, you see that most studies are based on self-report questionnaires on personality traits, mental health, and life satisfaction. What you don’t find is any data on actual (mental or physical) health measures, and no experiments. You therefore decide to make a bold claim come up with the carefully thought-through hypothesis that it’s maybe the lifestyle of the dog owners, which includes walking their dog several times per day, engaging in fun and healthy activities such as agility competitions, and taking them on trips, that gives them that extra boost in happiness. You could therefore answer your question in the following way:

Dog owners are happier than cat owners because of the dog-related activities they engage in.

Now you have to verify that your hypothesis fulfills the two requirements we introduced at the beginning of this resource article: falsifiability and testability . If it can’t be wrong and can’t be tested, it’s not a hypothesis. We are lucky, however, because yes, we can test whether owning a dog but not engaging in any of those activities leads to lower levels of happiness or well-being than owning a dog and playing and running around with them or taking them on trips.

## Writing a Hypothesis Step 3:

Make your predictions and define your variables. We have verified that we can test our hypothesis, but now we have to define all the relevant variables, design our experiment or data analysis, and make precise predictions. You could, for example, decide to study dog owners (not surprising at this point), let them fill in questionnaires about their lifestyle as well as their life satisfaction (as other studies did), and then compare two groups of active and inactive dog owners. Alternatively, if you want to go beyond the data that earlier studies produced and analyzed and directly manipulate the activity level of your dog owners to study the effect of that manipulation, you could invite them to your lab, select groups of participants with similar lifestyles, make them change their lifestyle (e.g., couch potato dog owners start agility classes, very active ones have to refrain from any fun activities for a certain period of time) and assess their happiness levels before and after the intervention. In both cases, your independent variable would be “ level of engagement in fun activities with dog” and your dependent variable would be happiness or well-being .

## Examples of a Good and Bad Hypothesis

Let’s look at a few examples of good and bad hypotheses to get you started.

## Good Hypothesis Examples

Bad hypothesis examples, tips for writing a research hypothesis.

If you understood the distinction between a hypothesis and a prediction we made at the beginning of this article, then you will have no problem formulating your hypotheses and predictions correctly. To refresh your memory: We have to (1) look at existing evidence, (2) come up with a hypothesis, (3) make a prediction, and (4) design an experiment. For example, you could summarize your dog/happiness study like this:

(1) While research suggests that dog owners are happier than cat owners, there are no reports on what factors drive this difference. (2) We hypothesized that it is the fun activities that many dog owners (but very few cat owners) engage in with their pets that increases their happiness levels. (3) We thus predicted that preventing very active dog owners from engaging in such activities for some time and making very inactive dog owners take up such activities would lead to an increase and decrease in their overall self-ratings of happiness, respectively. (4) To test this, we invited dog owners into our lab, assessed their mental and emotional well-being through questionnaires, and then assigned them to an “active” and an “inactive” group, depending on…

Note that you use “we hypothesize” only for your hypothesis, not for your experimental prediction, and “would” or “if – then” only for your prediction, not your hypothesis. A hypothesis that states that something “would” affect something else sounds as if you don’t have enough confidence to make a clear statement—in which case you can’t expect your readers to believe in your research either. Write in the present tense, don’t use modal verbs that express varying degrees of certainty (such as may, might, or could ), and remember that you are not drawing a conclusion while trying not to exaggerate but making a clear statement that you then, in a way, try to disprove . And if that happens, that is not something to fear but an important part of the scientific process.

Similarly, don’t use “we hypothesize” when you explain the implications of your research or make predictions in the conclusion section of your manuscript, since these are clearly not hypotheses in the true sense of the word. As we said earlier, you will find that many authors of academic articles do not seem to care too much about these rather subtle distinctions, but thinking very clearly about your own research will not only help you write better but also ensure that even that infamous Reviewer 2 will find fewer reasons to nitpick about your manuscript.

## Perfect Your Manuscript With Professional Editing

Now that you know how to write a strong research hypothesis for your research paper, you might be interested in our free AI proofreader , Wordvice AI, which finds and fixes errors in grammar, punctuation, and word choice in academic texts. Or if you are interested in human proofreading , check out our English editing services , including research paper editing and manuscript editing .

On the Wordvice academic resources website , you can also find many more articles and other resources that can help you with writing the other parts of your research paper , with making a research paper outline before you put everything together, or with writing an effective cover letter once you are ready to submit.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

## What is a Hypothesis – Types, Examples and Writing Guide

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Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

## Types of Hypothesis

Types of Hypothesis are as follows:

## Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

## Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

## Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

## Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

## Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

## Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

## Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

## Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

## Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

## Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

## Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

- Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
- Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
- Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
- Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
- Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
- Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

## How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

## Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

## Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

## Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

## Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

## Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

## Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

## Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

- Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
- Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
- Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
- Education : “Implementing a new teaching method will result in higher student achievement scores.”
- Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
- Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
- Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

## Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

## When to use Hypothesis

Here are some common situations in which hypotheses are used:

- In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
- In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
- I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

## Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

- Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
- Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
- Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
- Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
- Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
- Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
- Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

## Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

- Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
- Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
- Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
- Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
- Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
- Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

## Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

- Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
- May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
- May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
- Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
- Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
- May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

## About the author

## Muhammad Hassan

Researcher, Academic Writer, Web developer

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## How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

## What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study. Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

## What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

## Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

- Is the language clear and focused?
- What is the relationship between your hypothesis and your research topic?
- Is your hypothesis testable? If yes, then how?
- What are the possible explanations that you might want to explore?
- Does your hypothesis include both an independent and dependent variable?
- Can you manipulate your variables without hampering the ethical standards?
- Does your research predict the relationship and outcome?
- Is your research simple and concise (avoids wordiness)?
- Is it clear with no ambiguity or assumptions about the readers’ knowledge
- Is your research observable and testable results?
- Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

## Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

## 1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

## 2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

## 3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

## 4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

## Types of Research Hypothesis

The types of research hypothesis are stated below:

## 1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

## 2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

## 3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

## 4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

## 5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

## 6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

## 7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

## Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

## Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

- There must be a possibility to prove that the hypothesis is true.
- There must be a possibility to prove that the hypothesis is false.
- The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

## Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

This is awesome.Wow.

It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

clear and concise. thanks.

So Good so Amazing

Good to learn

Thanks a lot for explaining to my level of understanding

Explained well and in simple terms. Quick read! Thank you

It awesome. It has really positioned me in my research project

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General Education

Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including:

- Defining the term “hypothesis”
- Providing hypothesis examples
- Giving you tips for how to write your own hypothesis

So let’s get started!

## What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid.

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method . Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

- Observation
- Asking questions
- Forming a hypothesis
- Analyze the data
- Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

## Independent and Dependent Variables

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables: independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable.

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets.

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

## Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

## Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement!

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad. These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.

## The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

## #1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life:

- If I get enough sleep, I’ll be able to get more work done tomorrow.
- If the bus is on time, I can make it to my friend’s birthday party.
- If I study every night this week, I’ll get a better grade on my exam.

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades).

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

## #2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say:

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.”

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis!

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship.

## 4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

## #1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think.

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against science, as well. Take this hypothesis example:

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.”

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

## #2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible.

Good hypotheses ensure that you can observe the results.

## #3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable.

In writing your hypothesis, always keep in mind how you'll execute the experiment.

## #4: Generalizability

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

## Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

## Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come and how many leave. You also write down the temperature on the hour.

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

## Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like:

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

## Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment.

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this:

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

## Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while:

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again!

## Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

## What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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## 9.E: Hypothesis Testing with One Sample (Exercises)

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These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

## 9.1: Introduction

9.2: null and alternative hypotheses.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.

State the null hypothesis, \(H_{0}\), and the alternative hypothesis. \(H_{a}\), in terms of the appropriate parameter \((\mu \text{or} p)\).

- The mean number of years Americans work before retiring is 34.
- At most 60% of Americans vote in presidential elections.
- The mean starting salary for San Jose State University graduates is at least $100,000 per year.
- Twenty-nine percent of high school seniors get drunk each month.
- Fewer than 5% of adults ride the bus to work in Los Angeles.
- The mean number of cars a person owns in her lifetime is not more than ten.
- About half of Americans prefer to live away from cities, given the choice.
- Europeans have a mean paid vacation each year of six weeks.
- The chance of developing breast cancer is under 11% for women.
- Private universities' mean tuition cost is more than $20,000 per year.
- \(H_{0}: \mu = 34; H_{a}: \mu \neq 34\)
- \(H_{0}: p \leq 0.60; H_{a}: p > 0.60\)
- \(H_{0}: \mu \geq 100,000; H_{a}: \mu < 100,000\)
- \(H_{0}: p = 0.29; H_{a}: p \neq 0.29\)
- \(H_{0}: p = 0.05; H_{a}: p < 0.05\)
- \(H_{0}: \mu \leq 10; H_{a}: \mu > 10\)
- \(H_{0}: p = 0.50; H_{a}: p \neq 0.50\)
- \(H_{0}: \mu = 6; H_{a}: \mu \neq 6\)
- \(H_{0}: p ≥ 0.11; H_{a}: p < 0.11\)
- \(H_{0}: \mu \leq 20,000; H_{a}: \mu > 20,000\)

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:

- \(p < 0.30\)
- \(p \leq 0.30\)
- \(p \geq 0.30\)
- \(p > 0.30\)

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:

- \(p = 0.20\)
- \(p > 0.20\)
- \(p < 0.20\)
- \(p \leq 0.20\)

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:

- \(H_{0}: \bar{x} = 4.5, H_{a}: \bar{x} > 4.5\)
- \(H_{0}: \mu \geq 4.5, H_{a}: \mu < 4.5\)
- \(H_{0}: \mu = 4.75, H_{a}: \mu > 4.75\)
- \(H_{0}: \mu = 4.5, H_{a}: \mu > 4.5\)

## 9.3: Outcomes and the Type I and Type II Errors

State the Type I and Type II errors in complete sentences given the following statements.

- The mean number of cars a person owns in his or her lifetime is not more than ten.
- Private universities mean tuition cost is more than $20,000 per year.
- Type I error: We conclude that the mean is not 34 years, when it really is 34 years. Type II error: We conclude that the mean is 34 years, when in fact it really is not 34 years.
- Type I error: We conclude that more than 60% of Americans vote in presidential elections, when the actual percentage is at most 60%.Type II error: We conclude that at most 60% of Americans vote in presidential elections when, in fact, more than 60% do.
- Type I error: We conclude that the mean starting salary is less than $100,000, when it really is at least $100,000. Type II error: We conclude that the mean starting salary is at least $100,000 when, in fact, it is less than $100,000.
- Type I error: We conclude that the proportion of high school seniors who get drunk each month is not 29%, when it really is 29%. Type II error: We conclude that the proportion of high school seniors who get drunk each month is 29% when, in fact, it is not 29%.
- Type I error: We conclude that fewer than 5% of adults ride the bus to work in Los Angeles, when the percentage that do is really 5% or more. Type II error: We conclude that 5% or more adults ride the bus to work in Los Angeles when, in fact, fewer that 5% do.
- Type I error: We conclude that the mean number of cars a person owns in his or her lifetime is more than 10, when in reality it is not more than 10. Type II error: We conclude that the mean number of cars a person owns in his or her lifetime is not more than 10 when, in fact, it is more than 10.
- Type I error: We conclude that the proportion of Americans who prefer to live away from cities is not about half, though the actual proportion is about half. Type II error: We conclude that the proportion of Americans who prefer to live away from cities is half when, in fact, it is not half.
- Type I error: We conclude that the duration of paid vacations each year for Europeans is not six weeks, when in fact it is six weeks. Type II error: We conclude that the duration of paid vacations each year for Europeans is six weeks when, in fact, it is not.
- Type I error: We conclude that the proportion is less than 11%, when it is really at least 11%. Type II error: We conclude that the proportion of women who develop breast cancer is at least 11%, when in fact it is less than 11%.
- Type I error: We conclude that the average tuition cost at private universities is more than $20,000, though in reality it is at most $20,000. Type II error: We conclude that the average tuition cost at private universities is at most $20,000 when, in fact, it is more than $20,000.

For statements a-j in Exercise 9.109 , answer the following in complete sentences.

- State a consequence of committing a Type I error.
- State a consequence of committing a Type II error.

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is “the drug is unsafe.” What is the Type II Error?

- To conclude the drug is safe when in, fact, it is unsafe.
- Not to conclude the drug is safe when, in fact, it is safe.
- To conclude the drug is safe when, in fact, it is safe.
- Not to conclude the drug is unsafe when, in fact, it is unsafe.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

- at least 20%, when in fact, it is less than 20%.
- 20%, when in fact, it is 20%.
- less than 20%, when in fact, it is at least 20%.
- less than 20%, when in fact, it is less than 20%.

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average?

The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when, in fact, the mean number of hours

- is more than seven hours.
- is at most seven hours.
- is at least seven hours.
- is less than seven hours.

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:

- to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
- to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
- to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
- to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

## 9.4: Distribution Needed for Hypothesis Testing

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is \(\bar{X} \sim\) ________________

- \(N\left(7.24, \frac{1.93}{\sqrt{22}}\right)\)
- \(N\left(7.24, 1.93\right)\)

## 9.5: Rare Events, the Sample, Decision and Conclusion

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

- Is this a test of one mean or proportion?
- State the null and alternative hypotheses. \(H_{0}\) : ____________________ \(H_{a}\) : ____________________
- Is this a right-tailed, left-tailed, or two-tailed test?
- What symbol represents the random variable for this test?
- In words, define the random variable for this test.
- \(x =\) ________________
- \(n =\) ________________
- \(p′ =\) _____________
- Calculate \(\sigma_{x} =\) __________. Show the formula set-up.
- State the distribution to use for the hypothesis test.
- Find the \(p\text{-value}\).
- Reason for the decision:
- Conclusion (write out in a complete sentence):

## 9.6: Additional Information and Full Hypothesis Test Examples

For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in [link] . Please feel free to make copies of the solution sheets. For the online version of the book, it is suggested that you copy the .doc or the .pdf files.

If you are using a Student's \(t\) - distribution for one of the following homework problems, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, however.)

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using \(\alpha = 0.05\), is the data highly inconsistent with the claim?

- \(H_{0}: \mu \geq 50,000\)
- \(H_{a}: \mu < 50,000\)
- Let \(\bar{X} =\) the average lifespan of a brand of tires.
- normal distribution
- \(z = -2.315\)
- \(p\text{-value} = 0.0103\)
- Check student’s solution.
- alpha: 0.05
- Decision: Reject the null hypothesis.
- Reason for decision: The \(p\text{-value}\) is less than 0.05.
- Conclusion: There is sufficient evidence to conclude that the mean lifespan of the tires is less than 50,000 miles.
- \((43,537, 49,463)\)

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a standard deviation of 20¢. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95¢ with a standard deviation of 18¢. Do the data support the claim at the 1% level?

- \(H_{0}: \mu = $1.00\)
- \(H_{a}: \mu \neq $1.00\)
- Let \(\bar{X} =\) the average cost of a daily newspaper.
- \(z = –0.866\)
- \(p\text{-value} = 0.3865\)
- \(\alpha: 0.01\)
- Decision: Do not reject the null hypothesis.
- Reason for decision: The \(p\text{-value}\) is greater than 0.01.
- Conclusion: There is sufficient evidence to support the claim that the mean cost of daily papers is $1. The mean cost could be $1.
- \(($0.84, $1.06)\)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let \(x =\) the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?

- \(H_{0}: \mu = 10\)
- \(H_{a}: \mu \neq 10\)
- Let \(\bar{X}\) the mean number of sick days an employee takes per year.
- Student’s t -distribution
- \(t = –1.12\)
- \(p\text{-value} = 0.300\)
- \(\alpha: 0.05\)
- Reason for decision: The \(p\text{-value}\) is greater than 0.05.
- Conclusion: At the 5% significance level, there is insufficient evidence to conclude that the mean number of sick days is not ten.
- \((4.9443, 11.806)\)

In 1955, Life Magazine reported that the 25 year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 81 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was ten. Does it appear that the mean work week has increased for women at the 5% level?

Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think?

- \(H_{0}: p \geq 0.6\)
- \(H_{a}: p < 0.6\)
- Let \(P′ =\) the proportion of students who feel more enriched as a result of taking Elementary Statistics.
- normal for a single proportion
- \(p\text{-value} = 0.1308\)
- Conclusion: There is insufficient evidence to conclude that less than 60 percent of her students feel more enriched.

The “plus-4s” confidence interval is \((0.411, 0.648)\)

A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The average brown trout’s I.Q. is 4. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief.

Refer to Exercise 9.119 . Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout’s mean I.Q. is not four.

- \(H_{0}: \mu = 4\)
- \(H_{a}: \mu \neq 4\)
- Let \(\bar{X}\) the average I.Q. of a set of brown trout.
- two-tailed Student's t-test
- \(t = 1.95\)
- \(p\text{-value} = 0.076\)
- Reason for decision: The \(p\text{-value}\) is greater than 0.05
- Conclusion: There is insufficient evidence to conclude that the average IQ of brown trout is not four.
- \((3.8865,5.9468)\)

According to an article in Newsweek , the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7?

A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survey, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.

- \(H_{a}: p < 0.13\)
- Let \(P′ =\) the proportion of Americans who have seen or sensed angels
- –2.688
- \(p\text{-value} = 0.0036\)
- Reason for decision: The \(p\text{-value}\)e is less than 0.05.
- Conclusion: There is sufficient evidence to conclude that the percentage of Americans who have seen or sensed an angel is less than 13%.

The“plus-4s” confidence interval is (0.0022, 0.0978)

The mean work week for engineers in a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it’s shorter. She asks ten engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours?

Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.

Use the “Lap time” data for Lap 4 (see [link] ) to test the claim that Terri finishes Lap 4, on average, in less than 129 seconds. Use all twenty races given.

- \(H_{0}: \mu \geq 129\)
- \(H_{a}: \mu < 129\)
- Let \(\bar{X} =\) the average time in seconds that Terri finishes Lap 4.
- Student's t -distribution
- \(t = 1.209\)
- Conclusion: There is insufficient evidence to conclude that Terri’s mean lap time is less than 129 seconds.
- \((128.63, 130.37)\)

Use the “Initial Public Offering” data (see [link] ) to test the claim that the mean offer price was $18 per share. Do not use all the data. Use your random number generator to randomly survey 15 prices.

The following questions were written by past students. They are excellent problems!

"Asian Family Reunion," by Chau Nguyen

Every two years it comes around.

We all get together from different towns.

In my honest opinion,

It's not a typical family reunion.

Not forty, or fifty, or sixty,

But how about seventy companions!

The kids would play, scream, and shout

One minute they're happy, another they'll pout.

The teenagers would look, stare, and compare

From how they look to what they wear.

The men would chat about their business

That they make more, but never less.

Money is always their subject

And there's always talk of more new projects.

The women get tired from all of the chats

They head to the kitchen to set out the mats.

Some would sit and some would stand

Eating and talking with plates in their hands.

Then come the games and the songs

And suddenly, everyone gets along!

With all that laughter, it's sad to say

That it always ends in the same old way.

They hug and kiss and say "good-bye"

And then they all begin to cry!

I say that 60 percent shed their tears

But my mom counted 35 people this year.

She said that boys and men will always have their pride,

So we won't ever see them cry.

I myself don't think she's correct,

So could you please try this problem to see if you object?

- \(H_{0}: p = 0.60\)
- \(H_{a}: p < 0.60\)
- Let \(P′ =\) the proportion of family members who shed tears at a reunion.
- –1.71
- Reason for decision: \(p\text{-value} < \alpha\)
- Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of family members who shed tears at a reunion is less than 0.60. However, the test is weak because the \(p\text{-value}\) and alpha are quite close, so other tests should be done.
- We are 95% confident that between 38.29% and 61.71% of family members will shed tears at a family reunion. \((0.3829, 0.6171)\). The“plus-4s” confidence interval (see chapter 8) is \((0.3861, 0.6139)\)

Note that here the “large-sample” \(1 - \text{PropZTest}\) provides the approximate \(p\text{-value}\) of 0.0438. Whenever a \(p\text{-value}\) based on a normal approximation is close to the level of significance, the exact \(p\text{-value}\) based on binomial probabilities should be calculated whenever possible. This is beyond the scope of this course.

"The Problem with Angels," by Cyndy Dowling

Although this problem is wholly mine,

The catalyst came from the magazine, Time.

On the magazine cover I did find

The realm of angels tickling my mind.

Inside, 69% I found to be

In angels, Americans do believe.

Then, it was time to rise to the task,

Ninety-five high school and college students I did ask.

Viewing all as one group,

Random sampling to get the scoop.

So, I asked each to be true,

"Do you believe in angels?" Tell me, do!

Hypothesizing at the start,

Totally believing in my heart

That the proportion who said yes

Would be equal on this test.

Lo and behold, seventy-three did arrive,

Out of the sample of ninety-five.

Now your job has just begun,

Solve this problem and have some fun.

"Blowing Bubbles," by Sondra Prull

Studying stats just made me tense,

I had to find some sane defense.

Some light and lifting simple play

To float my math anxiety away.

Blowing bubbles lifts me high

Takes my troubles to the sky.

POIK! They're gone, with all my stress

Bubble therapy is the best.

The label said each time I blew

The average number of bubbles would be at least 22.

I blew and blew and this I found

From 64 blows, they all are round!

But the number of bubbles in 64 blows

Varied widely, this I know.

20 per blow became the mean

They deviated by 6, and not 16.

From counting bubbles, I sure did relax

But now I give to you your task.

Was 22 a reasonable guess?

Find the answer and pass this test!

- \(H_{0}: \mu \geq 22\)
- \(H_{a}: \mu < 22\)
- Let \(\bar{X} =\) the mean number of bubbles per blow.
- –2.667
- \(p\text{-value} = 0.00486\)
- Conclusion: There is sufficient evidence to conclude that the mean number of bubbles per blow is less than 22.
- \((18.501, 21.499)\)

"Dalmatian Darnation," by Kathy Sparling

A greedy dog breeder named Spreckles

Bred puppies with numerous freckles

The Dalmatians he sought

Possessed spot upon spot

The more spots, he thought, the more shekels.

His competitors did not agree

That freckles would increase the fee.

They said, “Spots are quite nice

But they don't affect price;

One should breed for improved pedigree.”

The breeders decided to prove

This strategy was a wrong move.

Breeding only for spots

Would wreak havoc, they thought.

His theory they want to disprove.

They proposed a contest to Spreckles

Comparing dog prices to freckles.

In records they looked up

One hundred one pups:

Dalmatians that fetched the most shekels.

They asked Mr. Spreckles to name

An average spot count he'd claim

To bring in big bucks.

Said Spreckles, “Well, shucks,

It's for one hundred one that I aim.”

Said an amateur statistician

Who wanted to help with this mission.

“Twenty-one for the sample

Standard deviation's ample:

They examined one hundred and one

Dalmatians that fetched a good sum.

They counted each spot,

Mark, freckle and dot

And tallied up every one.

Instead of one hundred one spots

They averaged ninety six dots

Can they muzzle Spreckles’

Obsession with freckles

Based on all the dog data they've got?

"Macaroni and Cheese, please!!" by Nedda Misherghi and Rachelle Hall

As a poor starving student I don't have much money to spend for even the bare necessities. So my favorite and main staple food is macaroni and cheese. It's high in taste and low in cost and nutritional value.

One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! $2.02 !!! Can you believe it? It made me stop and think. The world is changing fast. I had thought that the mean cost of a box (the normal size, not some super-gigantic-family-value-pack) was at most $1, but now I wasn't so sure. However, I was determined to find out. I went to 53 of the closest grocery stores and surveyed the prices of macaroni and cheese. Here are the data I wrote in my notebook:

Price per box of Mac and Cheese:

- 5 stores @ $2.02
- 15 stores @ $0.25
- 3 stores @ $1.29
- 6 stores @ $0.35
- 4 stores @ $2.27
- 7 stores @ $1.50
- 5 stores @ $1.89
- 8 stores @ 0.75.

I could see that the cost varied but I had to sit down to figure out whether or not I was right. If it does turn out that this mouth-watering dish is at most $1, then I'll throw a big cheesy party in our next statistics lab, with enough macaroni and cheese for just me. (After all, as a poor starving student I can't be expected to feed our class of animals!)

- \(H_{0}: \mu \leq 1\)
- \(H_{a}: \mu > 1\)
- Let \(\bar{X} =\) the mean cost in dollars of macaroni and cheese in a certain town.
- Student's \(t\)-distribution
- \(t = 0.340\)
- \(p\text{-value} = 0.36756\)
- Conclusion: The mean cost could be $1, or less. At the 5% significance level, there is insufficient evidence to conclude that the mean price of a box of macaroni and cheese is more than $1.
- \((0.8291, 1.241)\)

"William Shakespeare: The Tragedy of Hamlet, Prince of Denmark," by Jacqueline Ghodsi

THE CHARACTERS (in order of appearance):

- HAMLET, Prince of Denmark and student of Statistics
- POLONIUS, Hamlet’s tutor
- HOROTIO, friend to Hamlet and fellow student

Scene: The great library of the castle, in which Hamlet does his lessons

(The day is fair, but the face of Hamlet is clouded. He paces the large room. His tutor, Polonius, is reprimanding Hamlet regarding the latter’s recent experience. Horatio is seated at the large table at right stage.)

POLONIUS: My Lord, how cans’t thou admit that thou hast seen a ghost! It is but a figment of your imagination!

HAMLET: I beg to differ; I know of a certainty that five-and-seventy in one hundred of us, condemned to the whips and scorns of time as we are, have gazed upon a spirit of health, or goblin damn’d, be their intents wicked or charitable.

POLONIUS If thou doest insist upon thy wretched vision then let me invest your time; be true to thy work and speak to me through the reason of the null and alternate hypotheses. (He turns to Horatio.) Did not Hamlet himself say, “What piece of work is man, how noble in reason, how infinite in faculties? Then let not this foolishness persist. Go, Horatio, make a survey of three-and-sixty and discover what the true proportion be. For my part, I will never succumb to this fantasy, but deem man to be devoid of all reason should thy proposal of at least five-and-seventy in one hundred hold true.

HORATIO (to Hamlet): What should we do, my Lord?

HAMLET: Go to thy purpose, Horatio.

HORATIO: To what end, my Lord?

HAMLET: That you must teach me. But let me conjure you by the rights of our fellowship, by the consonance of our youth, but the obligation of our ever-preserved love, be even and direct with me, whether I am right or no.

(Horatio exits, followed by Polonius, leaving Hamlet to ponder alone.)

(The next day, Hamlet awaits anxiously the presence of his friend, Horatio. Polonius enters and places some books upon the table just a moment before Horatio enters.)

POLONIUS: So, Horatio, what is it thou didst reveal through thy deliberations?

HORATIO: In a random survey, for which purpose thou thyself sent me forth, I did discover that one-and-forty believe fervently that the spirits of the dead walk with us. Before my God, I might not this believe, without the sensible and true avouch of mine own eyes.

POLONIUS: Give thine own thoughts no tongue, Horatio. (Polonius turns to Hamlet.) But look to’t I charge you, my Lord. Come Horatio, let us go together, for this is not our test. (Horatio and Polonius leave together.)

HAMLET: To reject, or not reject, that is the question: whether ‘tis nobler in the mind to suffer the slings and arrows of outrageous statistics, or to take arms against a sea of data, and, by opposing, end them. (Hamlet resignedly attends to his task.)

(Curtain falls)

"Untitled," by Stephen Chen

I've often wondered how software is released and sold to the public. Ironically, I work for a company that sells products with known problems. Unfortunately, most of the problems are difficult to create, which makes them difficult to fix. I usually use the test program X, which tests the product, to try to create a specific problem. When the test program is run to make an error occur, the likelihood of generating an error is 1%.

So, armed with this knowledge, I wrote a new test program Y that will generate the same error that test program X creates, but more often. To find out if my test program is better than the original, so that I can convince the management that I'm right, I ran my test program to find out how often I can generate the same error. When I ran my test program 50 times, I generated the error twice. While this may not seem much better, I think that I can convince the management to use my test program instead of the original test program. Am I right?

- \(H_{0}: p = 0.01\)
- \(H_{a}: p > 0.01\)
- Let \(P′ =\) the proportion of errors generated
- Normal for a single proportion
- Decision: Reject the null hypothesis
- Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of errors generated is more than 0.01.

The“plus-4s” confidence interval is \((0.004, 0.144)\).

"Japanese Girls’ Names"

by Kumi Furuichi

It used to be very typical for Japanese girls’ names to end with “ko.” (The trend might have started around my grandmothers’ generation and its peak might have been around my mother’s generation.) “Ko” means “child” in Chinese characters. Parents would name their daughters with “ko” attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko—happy child, Yoshiko—a good child, Yasuko—a healthy child, and so on.

However, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with “ko.” More and more, parents seem to have become creative, modernized, and, sometimes, westernized in naming their children.

I have a feeling that, while 70 percent or more of my mother’s generation would have names with “ko” at the end, the proportion has dropped among my peers. I wrote down all my Japanese friends’, ex-classmates’, co-workers, and acquaintances’ names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has dropped for this generation.

Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako, Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko, Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko, Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko, Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko.

"Phillip’s Wish," by Suzanne Osorio

My nephew likes to play

Chasing the girls makes his day.

He asked his mother

If it is okay

To get his ear pierced.

She said, “No way!”

To poke a hole through your ear,

Is not what I want for you, dear.

He argued his point quite well,

Says even my macho pal, Mel,

Has gotten this done.

It’s all just for fun.

C’mon please, mom, please, what the hell.

Again Phillip complained to his mother,

Saying half his friends (including their brothers)

Are piercing their ears

And they have no fears

He wants to be like the others.

She said, “I think it’s much less.

We must do a hypothesis test.

And if you are right,

I won’t put up a fight.

But, if not, then my case will rest.”

We proceeded to call fifty guys

To see whose prediction would fly.

Nineteen of the fifty

Said piercing was nifty

And earrings they’d occasionally buy.

Then there’s the other thirty-one,

Who said they’d never have this done.

So now this poem’s finished.

Will his hopes be diminished,

Or will my nephew have his fun?

- \(H_{0}: p = 0.50\)
- \(H_{a}: p < 0.50\)
- Let \(P′ =\) the proportion of friends that has a pierced ear.
- –1.70
- \(p\text{-value} = 0.0448\)
- Reason for decision: The \(p\text{-value}\) is less than 0.05. (However, they are very close.)
- Conclusion: There is sufficient evidence to support the claim that less than 50% of his friends have pierced ears.
- Confidence Interval: \((0.245, 0.515)\): The “plus-4s” confidence interval is \((0.259, 0.519)\).

"The Craven," by Mark Salangsang

Once upon a morning dreary

In stats class I was weak and weary.

Pondering over last night’s homework

Whose answers were now on the board

This I did and nothing more.

While I nodded nearly napping

Suddenly, there came a tapping.

As someone gently rapping,

Rapping my head as I snore.

Quoth the teacher, “Sleep no more.”

“In every class you fall asleep,”

The teacher said, his voice was deep.

“So a tally I’ve begun to keep

Of every class you nap and snore.

The percentage being forty-four.”

“My dear teacher I must confess,

While sleeping is what I do best.

The percentage, I think, must be less,

A percentage less than forty-four.”

This I said and nothing more.

“We’ll see,” he said and walked away,

And fifty classes from that day

He counted till the month of May

The classes in which I napped and snored.

The number he found was twenty-four.

At a significance level of 0.05,

Please tell me am I still alive?

Or did my grade just take a dive

Plunging down beneath the floor?

Upon thee I hereby implore.

Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

- \(H_{0}: p = 0.40\)
- \(H_{a}: p < 0.40\)
- Let \(P′ =\) the proportion of schoolmates who fear public speaking.
- –1.01
- \(p\text{-value} = 0.1563\)
- Conclusion: There is insufficient evidence to support the claim that less than 40% of students at the school fear public speaking.
- Confidence Interval: \((0.3241, 0.4240)\): The “plus-4s” confidence interval is \((0.3257, 0.4250)\).

Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. To test if 68% also represents California’s percent for full-time faculty teaching the online classes, Long Beach City College (LBCC) in California, was randomly selected for comparison. In the same year, 34 of the 44 online courses LBCC offered were taught by full-time faculty. Conduct a hypothesis test to determine if 68% represents California. NOTE: For more accurate results, use more California community colleges and this past year's data.

According to an article in Bloomberg Businessweek , New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year’s rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

- \(H_{0}: p = 0.14\)
- \(H_{a}: p < 0.14\)
- Let \(P′ =\) the proportion of NYC residents that smoke.
- –0.2756
- \(p\text{-value} = 0.3914\)
- At the 5% significance level, there is insufficient evidence to conclude that the proportion of NYC residents who smoke is less than 0.14.
- Confidence Interval: \((0.0502, 0.2070)\): The “plus-4s” confidence interval (see chapter 8) is \((0.0676, 0.2297)\).

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test.

- \(H_{0}: \mu = 69,110\)
- \(H_{0}: \mu > 69,110\)
- Let \(\bar{X} =\) the mean salary in dollars for California registered nurses.
- \(t = 1.719\)
- \(p\text{-value}: 0.0466\)
- Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the mean salary of California registered nurses exceeds $69,110.
- \(($68,757, $73,485)\)

La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old.

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

- Reject \(H_{0}\): There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
- Do not reject \(H_{0}\): There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.
- Do not reject \(H_{0}\): There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
- Reject \(H_{0}\): There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing.

At a 1% level of significance, an appropriate conclusion is:

- There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.
- There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is more than 20%.
- There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.
- There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%.

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

At a significance level of \(a = 0.05\), what is the correct conclusion?

- There is enough evidence to conclude that the mean number of hours is more than 4.75
- There is enough evidence to conclude that the mean number of hours is more than 4.5
- There is not enough evidence to conclude that the mean number of hours is more than 4.5
- There is not enough evidence to conclude that the mean number of hours is more than 4.75

Instructions: For the following ten exercises,

Hypothesis testing: For the following ten exercises, answer each question.

State the null and alternate hypothesis.

State the \(p\text{-value}\).

State \(\alpha\).

What is your decision?

Write a conclusion.

Answer any other questions asked in the problem.

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

- \(H_{0}: p = 0.488\) \(H_{a}: p \neq 0.488\)
- \(p\text{-value} = 0.0114\)
- \(\alpha = 0.05\)
- Reject the null hypothesis.
- At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks.
- The survey does not appear to be accurate.

Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using \(\alpha = 0.05\), is the AAA proportion accurate?

The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. Does the evidence support the claim for Kentucky at the \(\alpha = 0.05\) level in Kentucky? Are the results applicable across the country? Why?

- \(H_{0}: p = 0.517\) \(H_{0}: p \neq 0.517\)
- \(p\text{-value} = 0.9203\).
- \(\alpha = 0.05\).
- Do not reject the null hypothesis.
- At the 5% significance level, there is not enough evidence to conclude that the proportion of homes in Kentucky that are heated by natural gas is 0.517.
- However, we cannot generalize this result to the entire nation. First, the sample’s population is only the state of Kentucky. Second, it is reasonable to assume that homes in the extreme north and south will have extreme high usage and low usage, respectively. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation.

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use \(\alpha = 0.01\) level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the \(\alpha = 0.05 level\), can it be concluded that the mean rainfall was below the reported average? What if \(\alpha = 0.01\)? Assume the amount of summer rainfall follows a normal distribution.

- \(H_{0}: \mu \geq 11.52\) \(H_{a}: \mu < 11.52\)
- \(p\text{-value} = 0.000002\) which is almost 0.
- At the 5% significance level, there is enough evidence to conclude that the mean amount of summer rain in the northeaster US is less than 11.52 inches, on average.
- We would make the same conclusion if alpha was 1% because the \(p\text{-value}\) is almost 0.

A survey in the N.Y. Times Almanac finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. The Austin, TX chamber of commerce feels that Austin’s commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters is 22.1 minutes with a standard deviation of 5.3 minutes. At the \(\alpha = 0.10\) level, is the Austin, TX commute significantly less than the mean commute time for the 15 largest US cities?

A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 times each year. A random sample of 20 women results in these yearly visit totals

3; 2; 1; 3; 7; 2; 9; 4; 6; 6; 8; 0; 5; 6; 4; 2; 1; 3; 4; 1

At the \(\alpha = 0.05\) level can it be concluded that the sample mean is higher than 5.8 visits per year?

- \(H_{0}: \mu \leq 5.8\) \(H_{a}: \mu > 5.8\)
- \(p\text{-value} = 0.9987\)
- At the 5% level of significance, there is not enough evidence to conclude that a woman visits her doctor, on average, more than 5.8 times a year.

According to the N.Y. Times Almanac the mean family size in the U.S. is 3.18. A sample of a college math class resulted in the following family sizes:

5; 4; 5; 4; 4; 3; 6; 4; 3; 3; 5; 5; 6; 3; 3; 2; 7; 4; 5; 2; 2; 2; 3; 2

At \(\alpha = 0.05\) level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?

The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At α = 0.01 level, is the student academic group’s claim correct?

- \(H_{0}: \mu \geq 150\) \(H_{0}: \mu < 150\)
- \(p\text{-value} = 0.0622\)
- \(\alpha = 0.01\)
- At the 1% significance level, there is not enough evidence to conclude that freshmen students study less than 2.5 hours per day, on average.
- The student academic group’s claim appears to be correct.

## 9.7: Hypothesis Testing of a Single Mean and Single Proportion

- Physics Concept Questions And Answers

## Hypothesis Questions

In physics, a hypothesis is a probable explanation for a physical phenomenon. Researchers usually base scientific hypotheses on earlier experiments or observations that cannot evidently be described with the existing scientific theories. At times the words “theory” and hypothesis are used interchangeably. However, a scientific theory is not the same as a scientific hypothesis.

## Important Hypothesis Questions with Answers

1) What is a hypothesis?

In science, a hypothesis is a structured assumption that is constructed based on some theoretical or experimental evidence. This is the first step during any research that transforms the investigation queries into predictions. It comprises components like population, variables and the relationship among the variables. Generally, a research hypothesis is a type of hypothesis that is employed to test the connection between multiple variables. For concrete evaluation, the developer of a hypothesis must be able to put forward specifics in functional terms. A hypothesis demands more work by the investigator for both confirming or disproving it. In this process, a confirmed hypothesis could become part of a probable theory or develop into a theory itself. Typically, a scientific hypothesis has the architecture of a mathematical model.

2) Give the fundamental types of hypotheses.

There are mainly six types of hypotheses:

- Simple hypothesis
- Complex hypothesis
- Directional hypothesis
- Non-directional hypothesis
- Null hypothesis
- Associative and causal hypothesis

3) What is meant by a directional hypothesis?

A directional hypothesis is a construct assumption derived by a researcher regarding a negative or positive change, difference, or relationship between two variables among a population. Typically, this prediction is based on previous research, extensive experience or accepted theory. The connection between the variables can also forecast its characteristics. For example, a middle-aged man exercising daily over time has a much lower chance of cardiac arrest than a man who does not follow any exercise routine.

4) What is meant by a non-directional hypothesis?

It is developed when there is no existing theory involved. In most cases, it is a statement that a connection lies between two variables without assuming the exact characteristics (direction) of the inherent connection.

5) What is a theory?

A theory is a scientific method that tries to explain the natural phenomena of the Universe by applying a consistent, systematic, logical way of investigation, data extraction, data scrutiny, experimenting, and refinement to reach a well-tested, thorough explanation that is concretely supported by proofs and evidence.

6) What are the main steps to developing a scientific theory?

Below is a generalised sequence of steps taken to develop a scientific theory:

- Choose and define the natural phenomenon that you need to figure out and describe. Gather data about this phenomenon by examining the source of the phenomena and analysing observations. We can also replicate this phenomenon by an experiment or simulation under a controlled environment (typically inside a laboratory) that removes interference from outside variables.
- After extracting sufficient data, analyse for repeating patterns in the data. Try to describe these recurring patterns by constructing a provisional explanation (hypothesis).
- Test the hypothesis by deriving more information to examine if the hypothesis stays true to exhibit the probable pattern. If the available data does not support the hypothesis, it must be altered or removed for a better one. During the collection of data, we must not ignore information that conflicts with the hypothesis in favour of only supportive information (known as “cherry-picking”). This is frequently misused by pseudo-scientists trying to scam people who are not familiar with scientific methodologies.
- If a concrete hypothesis stands true after all the scrutiny and is the most sound explanation for the phenomenon, then it is considered a valid theory. An established theory may undergo modifications and rejection if there exist enough pieces of evidence that contradict it. Thus, a theory is not a perpetual or absolute truth.

6) What are the main outcomes of a valid hypothesis?

Any valid hypothesis will allow us to make predictions by simple or deductive reasoning. In some scenarios, it could predict the result of a test in a laboratory or the probable observation of a natural process in the Universe. The prediction may give rise to statistics that further point to other extended probabilities or patterns. The scientific method comprises experimentation to validate the hypothesis to sufficiently explain the reasons under thorough investigation.

7) What are the main criteria for formulating a legitimate hypothesis?

During the development of a hypothesis, the researcher must not currently have an absolute prejudice over the probable result of the test or experiment. It should stay reasonably under the scope of the investigation. Then only the experiment or examination increases the probability of deriving a valid, true side of the hypothesis. If the investigator already knows the result, it is only considered a “consequence” (the investigator should have already taken this during the construction of the hypothesis). If the researcher cannot examine the predictions by experience or observation, the hypothesis must be tested by other qualified investigators providing observations.

Investigators examining alternative hypotheses may consider the following:

- Testability
- Parsimony – discouraging the postulation of unrestricted numbers of entities.
- Scope – the apparent application of the hypothesis to many scenarios of the phenomena.
- Fruitfulness – the potential that a hypothesis may help further explain phenomena in the future
- Conservatism – the compatibility with existing recognised knowledge systems.

8) What is a working hypothesis?

A working hypothesis is a type of hypothesis that is scientifically accepted as a foundation for further study in the hope that a plausible theory will be derived, even if the hypothesis eventually fails. Just like most hypotheses, a working hypothesis is created as a statement of assumptions, which can be connected to the exploratory investigation purpose in empirical analysis. They are often employed as an abstract foundation in qualitative research.

## Practice Questions

1) What is a postulate? 2) What is the difference between a hypothesis and a theory? 3) What is a pseudo-hypothesis? 4) Define a scientific theory.

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## Everyday life and its variability influenced human evolution at least as much as rare activities like big-game hunting

Professor and Chair of Biology at Seattle Pacific University and Affiliate Assistant Professor of Anthropology, University of Washington

## Disclosure statement

Cara Wall-Scheffler does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

University of Washington provides funding as a member of The Conversation US.

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Think about taking a walk: where you need to go, how fast you need to move to get there, and whether you need to bring something along to carry the results of your errand.

Are you going on this walk with someone else? Does walking with a friend change your preparation? If you’re walking with a child, do you remember to bring an extra sweater or a snack? You probably did – because people intuitively vary their plan depending on their current needs and situations.

In my research as an anthropologist , I’ve focused on the evolution of human walking and running because I love the flexibility people bring to these behaviors. Humans in all kinds of environments across space and time vary how far they go, when they go and what they go for – whether food, water or friends – based on a multitude of factors, including season, daylight, rituals and family.

Anthropologists split their studies of human activity into two broad categories: what people need to do – including eat, keep their kids alive and so on – and what solutions they come up with to accomplish these needs.

How people keep their children alive is a key issue in my research because it has a direct impact on whether a population survives. It turns out that kids stay alive if they’re with adults. To this end, it is a human universal that women carry heavy loads every day , including kids and their food. This needs-based behavior seems to have been an important part of our evolutionary history and explains quite a few aspects of human physiology and female morphology , such as women’s lower center of mass .

The solutions to other key problems, like specifically which food women will be carrying, vary across time and space. I suggest that these variations are as integral to explaining human biology and culture as the needs themselves.

## Impacts of uncommon activities

Evolutionary scientists often focus on how beneficial heritable traits get passed on to offspring when they provide a survival advantage. Eventually a trait can become more common in a population when it provides a useful solution.

For example, researchers have made big claims about how influential persistence hunting via endurance running has been on the way the human body evolved. This theory suggests that taking down prey by running them to exhaustion has led to humans’ own abilities to run long distances – by increasing humans’ ability to sweat, strengthening our head support and making sure our lower limbs are light and elastic.

But persistence hunting occurs in fewer than 2% of the recorded instances of hunting in one major ethnographic database , making it an extremely rare solution to the need to find food. Could such a rare and unusual form of locomotion have had a strong enough impact to select for the suite of adaptive traits that make humans such excellent endurance athletes today?

Maybe persistence hunting is actually a fallback strategy, providing a solution only at key moments when survivorship is on the edge. Or maybe these capabilities are just side effects of the loaded walking done every day . I think a better argument is that the ability to predict how to move between common and uncommon strategies has been the driver of human endurance capacity.

## Everyday life’s influence on evolution

Hunting itself, especially of large mammals, is hardly ubiquitous , despite how frequently it is discussed. For example, anthropologists tend to generalize that people who lived in the Arctic even up to a hundred years ago consumed only animal meat hunted by men. But actually, the original ethnographic work reveals a far more nuanced picture .

Women and children were actively involved in hunting, and it was a strongly seasonal activity. Coastal fishing, berry picking and the use of plant materials were all vital to Arctic people’s day-to-day sustenance. Small family groups used canoes for coastal foraging for part of the year.

During other seasons, the whole community participated in hunting large mammals by herding them into dangerous situations where they were more easily killed. Sometimes family groups were together, and sometimes large communities were together. Sometimes women hunted with rifles, and sometimes children ran after caribou.

The dynamic nature of daily life means that the relatively uncommon activity of hunting large terrestrial vertebrates is unlikely to be the main behavior that helps humans solve the key problems of food, water and keeping children alive.

Anthropologist Rebecca Bliege Bird has investigated how predictable food is throughout the day and the year . She’s noted that for most communities, big game is rarely caught, especially when a person is hunting alone. Even among the Hadza in Tanzania, generally considered a big-game hunting community, a hunter acquires 0.03 prey per day on average – essentially 11 animals a year for that person.

Bird and others clearly argue that the planning and flexible coordination done by females is the crucial aspect of how humans survive on a daily basis. It’s the daily efforts of females that allow people to be spontaneous a few times a year to accomplish high-risk activities such as hunting – persistence or otherwise. Therefore it is female flexibility that allows communities to survive between the rare big-game opportunities.

## Changing roles and contributions

Some anthropologists argue that in some parts of the world, behavior varies more for cultural reasons , like what tools you make, than for environmental ones, such as how much daylight there is during winter. The importance of culture means that the solutions vary more than the needs.

One of the aspects of culture that varies is the role assigned to specific genders. Varying gender roles are related to the distribution of labor and when people take on certain solution-based tasks . In most cultures, these roles change across a female’s life span. In American culture, this would be like a grandparent going back to college to hone a childhood passion in order to take on a new job to send their grandchildren to college.

In many places, females go from youth when they might carry their siblings and firewood, to early parenthood where they might go hunting with a baby on their back , to older parenthood where they might carry water on their head, a baby on their back and tools in their hands, to postmenopausal periods when they might carry giant loads of mangoes and firewood to and from camp.

Even though always load carrying , our capacity to plan and change our behavior for diverse environments is part of what drives Homo sapiens ’ success, which means that the behavior of females across their different life stages has been a major driver of this capability.

- Anthropology
- Human evolution
- Ethnography
- Women's bodies

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Learn how to formulate a hypothesis for your research project, based on a research question, existing theories and data. Find out how to phrase your hypothesis in different ways and write a null hypothesis for statistical testing.

The primary research question should originate from the hypothesis, not the data, and be established before starting the study. Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation ('x affects y because …'). A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses.

Creating a research hypothesis to answer a research problem is an iterative process. (Image by rawpixel.com on Freepik) Any research begins with a research question and a research hypothesis.A research question alone may not suffice to design the experiment(s) needed to answer it. A hypothesis is central to the scientific method. But what is a hypothesis?

INTRODUCTION. Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses.1,2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results.3,4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the ...

Learn how to write a strong research question for your academic paper, dissertation, or thesis. Find out what makes a good research question and see examples for different purposes and fields.

3. Simple hypothesis. A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, "Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking. 4.

Learn how to test hypotheses using statistics in 5 steps: state your null and alternate hypothesis, collect data, perform a statistical test, decide whether to reject or fail to reject your null hypothesis, and present your findings. See examples of hypothesis testing in different contexts and scenarios.

A good research question should: Be clear and provide specific information so readers can easily understand the purpose. Be focused in its scope and narrow enough to be addressed in the space allowed by your paper. Be relevant and concise and express your main ideas in as few words as possible, like a hypothesis.

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process. Consider a study designed to examine the relationship between sleep deprivation and test ...

Research hypothesis. The primary research question should be driven by the hypothesis rather than the data. 1, 2 That is, the research question and hypothesis should be developed before the start of the study. This sounds intuitive; however, if we take, for example, a database of information, it is potentially possible to perform multiple ...

"A hypothesis is a conjectural statement of the relation between two or more variables". (Kerlinger, 1956) "Hypothesis is a formal statement that presents the expected relationship between an independent and dependent variable."(Creswell, 1994) "A research question is essentially a hypothesis asked in the form of a question."

Formulate the Hypothesis; Based on your research question and preliminary research, now you can create your hypothesis. A good hypothesis should be clear, concise, and testable. It typically takes a statement form, predicting a potential outcome or relationship between variables. Make sure that your hypothesis is focused and answers your ...

Primarily, a research question, just like a hypothesis, is focused and concise. But a hypothesis includes a prediction based on the proposed research, and is designed to forecast the relationship of and between two (or more) variables. Research questions are open-ended, and invite debate and discussion, while hypotheses are closed, e.g. ...

Another example for a directional one-tailed alternative hypothesis would be that. H1: Attending private classes before important exams has a positive effect on performance. Your null hypothesis would then be that. H0: Attending private classes before important exams has no/a negative effect on performance.

Formulate the Hypothesis. Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence. Write the Null Hypothesis

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem. 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a 'if-then' structure. 3.

The first question asks for a ready-made solution, and is not focused or researchable. The second question is a clearer comparative question, but note that it may not be practically feasible. For a smaller research project or thesis, it could be narrowed down further to focus on the effectiveness of drunk driving laws in just one or two countries.

A hypothesis is all about asking a question. What Is a Hypothesis? Merriam Webster defines a hypothesis as "an assumption or concession made for the sake of argument." In other words, a hypothesis is an educated guess. Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it's true or not.

An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized-approximately 1,200 students-small city demographic) to determine if the local high school's percentage was lower. One hundred fifty students were chosen at random and surveyed.

Hypothesis Questions. In physics, a hypothesis is a probable explanation for a physical phenomenon. Researchers usually base scientific hypotheses on earlier experiments or observations that cannot evidently be described with the existing scientific theories. At times the words "theory" and hypothesis are used interchangeably.

View Solution to Question 1. Question 2. A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get the following scores:62, 92, 75 ...

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question. A hypothesis is not just a guess — it should be based on ...

Some anthropologists question how much rare activities like big-game hunting could have affected how our species evolved. Instead they're looking at daily activities like carrying water or firewood.