hypothesis in a small sentence

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HYPOTHESIS in a Sentence Examples: 21 Ways to Use Hypothesis

Have you ever wondered what a “hypothesis” is and how it fits into the scientific method? A hypothesis is a proposed explanation or educated guess that can be tested through research and experimentation to determine its validity.

In scientific inquiry, a hypothesis serves as the foundation for the study, guiding the direction of the research and helping to form conclusions based on the results. By formulating clear hypotheses, researchers can systematically investigate phenomena and gather evidence to support their claims.

Table of Contents

7 Examples Of Hypothesis Used In a Sentence For Kids

• Hypothesis is a guess we can test.
• We can make a hypothesis about what will happen.
• Our hypothesis will help us learn new things.
• Let’s think of a hypothesis to investigate.
• We can use our hypothesis to solve a problem.
• A good hypothesis can help us understand the world.
• Remember, our hypothesis is just a starting point.

14 Sentences with Hypothesis Examples

• Hypothesis : Students who study for at least 3 hours every day are likely to perform better in their exams.
• It is important for college students to form a hypothesis before conducting any research project.
• Hypothesis : Attending lectures regularly can significantly improve academic performance.
• College students can test their hypothesis through interactive experiments and surveys.
• Hypothesis : Using different study methods can have varied effects on information retention.
• It is necessary for students to critically analyze data to support or reject their hypothesis .
• Hypothesis : Students who engage in extracurricular activities may have a better overall college experience.
• In a scientific study, researchers must clearly define their hypothesis before proceeding with the experiment.
• Hypothesis : Regular exercise can positively impact a student’s mental health and academic performance.
• It is crucial for college students to document their hypothesis and research findings accurately.
• Hypothesis : Students who limit their social media usage may experience improved focus and productivity.
• College projects often require students to brainstorm and formulate a solid hypothesis .
• It is common for students to revise their hypothesis based on new information or research outcomes.
• Hypothesis : Implementing study breaks can enhance retention and understanding of complex subjects.

How To Use Hypothesis in Sentences?

Hypothesis is an educated guess or prediction that can be tested through observation or experimentation. When incorporating this term into a sentence, it is important to clearly identify it so readers can understand its significance.

Here are some tips on how to use hypothesis effectively in a sentence:

Clearly state your hypothesis in a simple and concise manner. For example, “The scientist’s hypothesis is that plants will grow faster with added sunlight.”

Use the word hypothesis to introduce your prediction or expectation before testing it. For instance, “Our hypothesis is that students who study regularly will perform better on the exam.”

Make sure to refer back to your hypothesis when discussing the results of your experiment. For example, “The data supported our initial hypothesis that exercise leads to improved cardiovascular health.”

You can also use the word hypothesis when comparing multiple predictions. For instance, “There are several hypotheses about the cause of the mysterious illness, but more research is needed to determine the correct one.”

By following these guidelines, you can effectively incorporate hypothesis into your writing to communicate your predictions or expectations clearly and accurately.

In conclusion, sentences with the keyword “hypothesis” often express a proposed explanation or prediction that can be tested through research or observation. These sentences play a crucial role in scientific inquiry by guiding investigations and exploring relationships between variables. For example, “The researchers formulated a hypothesis to predict the effect of sunlight on plant growth” demonstrates how hypotheses are used to frame a study’s objectives and outcomes.

Clear and concise sentences with hypotheses are essential for building a solid foundation for scientific exploration and discovery. They provide a starting point for experiments, helping researchers to structure their methodologies and draw meaningful conclusions. By carefully crafting hypotheses, scientists can effectively test their theories, gather evidence, and contribute to the advancement of knowledge in various fields.

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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 .

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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.

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Understanding a Hypothesis (Definition, Null, and Examples)

You come home exhausted and plop down on the couch. You don’t know why you are feeling so weary. You think about several possible reasons. Is it because you stayed up late last night? Is it because you skipped breakfast? Or is it because you had to take the stairs due to a power outage? Or is it because of all the above reasons?

What you are doing is hypothesizing about why you are feeling tired.

If you enjoy reading detective stories, you would have already come across a hypothesis. A good whodunit mystery confounds the reader with multiple hypotheses about who committed the crime.

• What is a Hypothesis?

The term hypothesis is often used in a scientific context as a possible explanation for an occurrence.

The word originated from ancient Greek and means “putting under” indicating its early association with experimentation.

A hypothesis is:

• An assumption that serves as a starting point for further research
• A supposition made on the basis of insufficient evidence
• A tentative and logical statement that can be tested for its authenticity
• An idea that seeks to explain why a phenomenon takes place
• A prediction about the outcome of a study according to known facts
• A proposal about the possible relationship between two or more variables

A scientist testing a hypothesis is no different from a detective investigating a crime scene. Famous detectives such as Sherlock Holmes combine the evidence with their powers of prediction to identify the criminal from several potential suspects.

The scientist examines each hypothesis rigorously for any inconsistencies through experiments before it can receive the stamp of approval.

Scientists accept a hypothesis as a theory only after it has been validated several times in different conditions. This includes use of scientific methods and protocols involving observation and analysis of results.

A good hypothesis seeks to establish a causal relationship between two or more variables, primarily between the independent and the dependent variable.

Brushing your teeth at least twice in a day reduces the incidence of dental caries.

The independent variable or cause in the above example is the number of times you brush in a day. The dependent variable or effect is the incidence of dental caries or cavities.

A scientist or researcher tests a hypothesis by changing the independent variable and measuring its effect on the dependent variable.

A relationship between a single independent and dependent variable is known as a simple hypothesis.

The mathematical expression of this relationship is:

• where x is the independent variable and Y is the dependent variable and
• where x is the input and Y is the output or a function of x

So, brushing your teeth at least twice daily is an input and the reduction of dental caries is an output or a function of the action of brushing your teeth. 

If there are multiple independent variables or in some cases more than a single dependent variable, the statement is a complex hypothesis.

Brushing your teeth at least twice a day and using dental floss reduces the incidence of cavities and periodontitis.

In the above example the two independent variables are brushing teeth and using dental floss. The dependent variables are reduction in cavities and periodontitis or gum infection. In this example the two independent variables are common for the two dependent variables.

The equation of a complex hypothesis can be written as:

Y = f(x 1 +x 2 +x 3 …)

Y 1 = f(z 1 +z 2 +z 3 …)

where z is a different set of independent variables for Y1 as the dependent variable

• Developing a Hypothesis

A hypothesis is a frame of reference or a window through which you observe a phenomenon. The phenomenon is the dependent variable. Your job is to determine the independent variables that are causing the event.

Cultivate the habit of looking for patterns in anything that happens. Train your mind to think in terms of stimulus and reaction or cause and effect.

This will enable you to glean insights from the knowledge you gather. You will then be able to write a strong hypothesis that focuses on the variables that matter over the noise.

The six steps to developing a hypothesis are:

• Ask a question
• Preliminary research
• Formulate the hypothesis
• Refine the hypothesis
• Phrase your hypothesis in three ways
• Write a null hypothesis

Ask a Question

The first step is to write a research question.

To write an effective research question be as curious as possible. Start with asking yourself a ton of questions.

Begin with broad and open-ended questions before narrowing it down to more specific ones.

You can use the 5W1H method to get into the mode of writing a research question.

• What took place?
• When did it happen?
• Where did it occur?
• Why did it take place?
• Who did it affect ?
• How did it happen?

The research question needs to be clear, objective , well-defined and measurable.

Do people who take health supplements log in fewer sick days at work in a year than those who don’t?

After you have framed the right question you can make an educated guess to answer it. This answer will be your preliminary hypothesis. Your hypothesis will attempt to answer the research question with observable facts through various experiments.

Preliminary Research

You don’t have to start from scratch. You can draw from preexisting knowledge and well-established theories to discount fallacious premises at the outset.

Resources that you can refer to include case studies, research papers and theses published in academic or scientific journals. A thorough background research will help you to look at the research question from several angles.

Do keep an open mind or a blank slate to avoid falling in the trap of preconceived notions and prejudices. Your initial research should help you focus on the areas where you are most likely to find the answers.

You can come up with a blueprint or outline highlighting the variables that you think are most relevant to your research question.

Think how changing the attributes of a single variable potentially affects others. You may need to operationalize or define how you are going to measure the variables and their effects.

Formulate the Hypothesis

It’s time now to put together your hypothesis into words.

A sound hypothesis states:

• Who or what is being studied?
• The relationship between the variables
• A measurable and reproducible outcome
• The possibility to prove it as true or false

Teenagers in the 14-16 age group who eat a high-protein diet are taller by two inches than the average height for that age group.

The next step is to ensure your statement ticks all the boxes for a strong hypothesis.

Is the hypothesis:

• Precise and quantifiable without any ambiguity
• Lucid and focused on the results described in the research question

Does the hypothesis include:

• An independent and dependent variable
• Variables that can be changed or controlled
• Terms that even a layman can understand
• A well-defined outcome

Phrase your Hypothesis in Three Ways

A hypothesis is often written in an If-then format. This format describes the cause and effect relationship between an independent variable and a dependent variable.

Phrase your hypothesis as “If {you make changes to an independent variable} then {you will observe this change in the dependent variable}.”

If employees are given more autonomy to take work-related decisions then their overall performance improves.

Another way to write a hypothesis is by directly stating the outcome between the two variables.

More autonomy in terms of taking work-related decisions helps to improve an employee’s overall performance.

You can also state a hypothesis as a comparison between two groups.

Employees who are offered more autonomy to take work-related decisions show better overall performance than those who work in a micro-managed environment.

Write a Null Hypothesis

The next step is to frame a null hypothesis, especially if your study requires you to analyze the data statistically. A null hypothesis by default takes a converse position to the researcher’s hypothesis.

Your statement is known as the alternative hypothesis while its opposite outcome is referred to as the null hypothesis.

If you expect a change according to a relationship between the variables the null hypothesis denies the possibility of any change or association between the variables. If you expect the conditions to remain constant the null hypothesis states that change will take place.

The null hypothesis is referred to as H 0. Your hypothesis which is the alternative is written as H 1 or H a .

H 1 : A player who is more than two meters tall has a better chance of winning the National Basketball Association Most Valuable Player Award.

H 0 : The height of a player does not affect his prospects of winning the National Basketball Association Most Valuable Player Award.

Hypothesis Examples

Examples of research questions.

• Which loop diuretic drug is more effective for treating heart failure?
• Does attending online learning sessions help students to improve their exam scores?
• Does talking on the phone while driving cause more accidents?
• Does increasing the pressure affect the rate of reaction between gases?
• Is a person more likely to be obese if she or he eats unhealthy foods at least four times in a week?

Examples of a Hypothesis

• The clinical trial of the new drug Furosemide proved that it is better at treating heart failure than other loop diuretic drugs such as Bumetanide.
• The students who attended online learning sessions had better exam scores than those who skipped the sessions.
• Drivers who talk on the phone are likely to have an accident than those who don’t.
• Increasing the pressure affects the concentration of gases and it acts as a catalyst in speeding up the rate of reaction.
• People who eat processed foods frequently are more likely to be obese than people who limit their intake of such foods.

Examples of a Null Hypothesis

• The clinical trial proved that there is no difference between the effectiveness of Furosemide and other loop diuretic drugs, such as Bumetanide, for treating heart failure.
• There is no difference in the exam scores of students who attended online learning sessions and those who did not attend.
• There is no difference in the rate of accidents experienced by drivers who talk on the phone compared with those who don’t talk on the phone while driving.
• The elevation of pressure has no effect on the rate of reaction between gases.
• The food consumed and its frequency of consumption do not affect the probability of a person becoming obese.

What are Null Hypotheses?

The null hypothesis states the opposite outcome to the researcher’s hypothesis.

In most cases, the null hypothesis’s default position is a prediction that no relationship exists between any two or more variables. The null hypothesis denies the possibility of a causal relationship existing between an assumed independent and dependent variable.

The symbol of the null hypothesis is H 0 .

The notion of a null hypothesis fulfills the requirement of the falsifiability of a hypothesis before it can be accepted as valid.

A null hypothesis is often written as a negative statement that posits that the original hypothesis is false. It either claims that the results obtained are due to chance or there is no evidence to prove any change.

Original Hypothesis: Use of nitrogen fertilizers helps plants grow faster as compared to use of phosphorus or potassium fertilizers. 

Null Hypothesis (H 0 ): The fertilizer used has no bearing on the rate of plant growth

What are Alternative Hypotheses?

An alternative hypothesis states the researcher’s supposition of a causal relationship between any two or more variables. Alternative hypotheses are based upon an observable effect and seek to predict how changing an independent variable will affect the dependent variable.

An alternative hypothesis is symbolized as H 1 or H a . It’s often written together with a null hypothesis with the two statements existing as a dual pair of opposite assumptions. Only a single statement among two can be true.

Alternative hypotheses try to determine that the results are obtained due to significant changes related to the variables and not due to chance.

Research Question: Does washing hands thoroughly with soap before eating a meal reduce the rate of recurrence of respiratory ailments?

Alternative Hypothesis (H 1 ): Washing hands with soap before eating reduces the rate of recurrence of respiratory ailments by 30% compared with those who neglect hand hygiene.

Null Hypothesis (H 0 ): Washing hands with soap before eating has no effect on the rate of recurrence of respiratory ailments. 

What is Hypothesis Testing?

After you have formulated a hypothesis, you need to choose a research and testing method.

Use a descriptive approach when experiments are difficult to conduct. A descriptive method incorporates case studies and surveys to collect data.

You can employ statistical tools such as a correlational study to measure the relationship between variables.

A correlational study calculates the probability of whether a linkage between two variables can be determined or do the changes occur purely due to chance. Do note that correlation is not equivalent to causality.

This method lets you arrive at a conclusion by generalizing the data obtained without performing any actual experiments. A hypothesis proved using this approach is known as a statistical hypothesis.

The other approach is the experimental method in which causal relationships are established between different variables through demonstrations. A working or empirical hypothesis often makes use of the experimental method to determine the relationships between the variables.

The steps for testing a hypothesis experimentally are:

• Design of experiments
• Collating data
• Analysis of observable facts
• Summarizing the conclusions
• Validating the hypothesis as a theory

How to Write a Good Hypothesis

To find ideas for a hypothesis, you can look through discussion sections in academic and scientific journals or browse online publications. You will come across questions that can be investigated further.

Simple Steps

The steps to write a strong hypothesis are:

• Choose your frame of reference or direction for determining the cause
• Such an approach is known as a directional hypothesis
• If you are unable to determine a starting point or the current theories are ambiguous and contradictory, you can choose a non-directional approach
• This method involves stating the facts and observations randomly and then seeking to find a pattern
• Identify the key variables
• A variable is any attribute that can have measurable values such as temperature, time, or length
• Tentatively label some variables as independent and some as dependent
• State the relationship between the variables using clear and objective language
• Operationalize or define how you will measure the variables for testability
• Write the statement in the If-then format. You can also write it as a declarative sentence
• Avoid jargon and use simple words that can be understood by a layman
• Write a null hypothesis to satisfy the condition of falsifiability

If you watch television for more than three hours a day, then your ability to concentrate diminishes.

How to Write a Scientific Hypothesis

A good scientific hypothesis is:

• Consistent: Use preexisting knowledge as a springboard for further research
• Testable: Include words that are quantifiable or measurable
• Concise: Cut down on verbose phrases and use precise words
• Scalable: Formulate the statement in a universal context based on the variables
• Promising: State unexplained occurrences as loose ends that can be investigated further

Simple steps

• Record your observations and facts about the topic
• Evaluate your statements for possible links to determine the cause and effect
• Document all potential explanations to analyze further
• Write the null hypothesis along with your own hypothesis
• This satisfies the requisite condition for a valid hypothesis. It can either be confirmed or disproved

If you plant cotton in black soil, then the production is boosted by 20% as compared to the output from red soil.

How to write a Psychology Hypothesis

A psychology hypothesis often begins with how the environment or certain parameters within it influence or cause a specific behavior.

To write a sound psychology hypothesis:

• Choose a topic that you are genuinely interested in
• Do not ramble. Keep it short and simple
• Use previous research and your own study to direct your vision
• Ascertain and define the variables
• You can write the hypothesis either as an If-then statement
• Other alternatives are to write the hypothesis as a direct sentence or a comparative supposition

Use the following questions to guide your understanding of the topic.

• Is your hypothesis based on a preexisting theory or your own research? 
• Can your hypothesis be tested for falsifiability?
• What are the independent and dependent variables?

People who exercise regularly are less at risk from depression than people who lead a sedentary life.

• What is and How to Write a Good Hypothesis in Research?
• How to Write a Hypothesis in 6 Steps
• Developing Hypothesis and Research Questions
• Forming a Good Hypothesis for Scientific Research
• 6 Hypothesis Examples in Psychology
• Correlational Research | When & How to Use
• How to Write a Strong Hypothesis in 6 Simple Steps
• How to Develop a Good Research Hypothesis
• How To Develop a Hypothesis (With Elements, Types and Examples)
• Definition of Hypothesis

Inside this article

Fact checked: Content is rigorously reviewed by a team of qualified and experienced fact checkers. Fact checkers review articles for factual accuracy, relevance, and timeliness. Learn more.

About the author

Dalia Y.: Dalia is an English Major and linguistics expert with an additional degree in Psychology. Dalia has featured articles on Forbes, Inc, Fast Company, Grammarly, and many more. She covers English, ESL, and all things grammar on GrammarBrain.

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Definition of hypothesis

Did you know.

The Difference Between Hypothesis and Theory

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

• proposition
• supposition

hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.

hypothesis implies insufficient evidence to provide more than a tentative explanation.

theory implies a greater range of evidence and greater likelihood of truth.

law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.

Examples of hypothesis in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do

1641, in the meaning defined at sense 1a

Phrases Containing hypothesis

• counter - hypothesis
• nebular hypothesis
• null hypothesis
• planetesimal hypothesis
• Whorfian hypothesis

Articles Related to hypothesis

This is the Difference Between a...

This is the Difference Between a Hypothesis and a Theory

In scientific reasoning, they're two completely different things

Dictionary Entries Near hypothesis

hypothermia

hypothesize

Cite this Entry

“Hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/hypothesis. Accessed 28 Apr. 2024.

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Kids definition of hypothesis, medical definition, medical definition of hypothesis, more from merriam-webster on hypothesis.

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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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What Are Examples of a Hypothesis?

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A hypothesis is an explanation for a set of observations. Here are examples of a scientific hypothesis.

Although you could state a scientific hypothesis in various ways, most hypotheses are either "If, then" statements or forms of the null hypothesis . The null hypothesis is sometimes called the "no difference" hypothesis. The null hypothesis is good for experimentation because it's simple to disprove. If you disprove a null hypothesis, that is evidence for a relationship between the variables you are examining.

Examples of Null Hypotheses

• Hyperactivity is unrelated to eating sugar.
• All daisies have the same number of petals.
• The number of pets in a household is unrelated to the number of people living in it.
• A person's preference for a shirt is unrelated to its color.

Examples of If, Then Hypotheses

• If you get at least 6 hours of sleep, you will do better on tests than if you get less sleep.
• If you drop a ball, it will fall toward the ground.
• If you drink coffee before going to bed, then it will take longer to fall asleep.
• If you cover a wound with a bandage, then it will heal with less scarring.

Improving a Hypothesis to Make It Testable

You may wish to revise your first hypothesis in order to make it easier to design an experiment to test. For example, let's say you have a bad breakout the morning after eating a lot of greasy food. You may wonder if there is a correlation between eating greasy food and getting pimples. You propose the hypothesis:

Eating greasy food causes pimples.

Next, you need to design an experiment to test this hypothesis. Let's say you decide to eat greasy food every day for a week and record the effect on your face. Then, as a control, you'll avoid greasy food for the next week and see what happens. Now, this is not a good experiment because it does not take into account other factors such as hormone levels, stress, sun exposure, exercise, or any number of other variables that might conceivably affect your skin.

The problem is that you cannot assign cause to your effect . If you eat french fries for a week and suffer a breakout, can you definitely say it was the grease in the food that caused it? Maybe it was the salt. Maybe it was the potato. Maybe it was unrelated to diet. You can't prove your hypothesis. It's much easier to disprove a hypothesis.

So, let's restate the hypothesis to make it easier to evaluate the data:

Getting pimples is unaffected by eating greasy food.

So, if you eat fatty food every day for a week and suffer breakouts and then don't break out the week that you avoid greasy food, you can be pretty sure something is up. Can you disprove the hypothesis? Probably not, since it is so hard to assign cause and effect. However, you can make a strong case that there is some relationship between diet and acne.

If your skin stays clear for the entire test, you may decide to accept your hypothesis . Again, you didn't prove or disprove anything, which is fine

• Null Hypothesis Definition and Examples
• What Is a Hypothesis? (Science)
• What Are the Elements of a Good Hypothesis?
• Understanding Simple vs Controlled Experiments
• What Is a Testable Hypothesis?
• What 'Fail to Reject' Means in a Hypothesis Test
• Null Hypothesis Examples
• How To Design a Science Fair Experiment
• Scientific Method Vocabulary Terms
• Scientific Hypothesis Examples
• Six Steps of the Scientific Method
• An Example of a Hypothesis Test
• Definition of a Hypothesis
• Scientific Method Flow Chart
• Null Hypothesis and Alternative Hypothesis

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A panoply of teaching resources.

Writing Hypothesis Sentences

Some English students have a hard time expressing complex ideas in short sentences. They don’t know how to summarize or synthesize information. This short lesson helps students overcome that barrier by teaching them how to construct a hypothesis with an easy to learn sentence pattern. 

Lesson Objectives

By the end of this lesson, students should be able to:

• define hypothesis
• use it to communicate and synthesize complex ideas

Student Level: intermediate +

Lesson time: 50-75 minutes

Extra resource: pdf file with images and suggested answers for class review .

Part 1. Overview: Hypothesis Sentence Pattern (10 minutes)

A hypothesis is a sentence which shows us how two different things are connected. There are many ways to write a hypothesis. This lessons focuses on one sentence pattern because it is easy to understand and use.

Here are some examples:

• The more water a plant gets, the faster the plant will grow.
• The more I study , the more I learn.
• The richer the country, the more waste is produced.
• The hotter the temperature , the more ice cream people buy.

When writing a hypothesis sentence, it is important to remember this:

• The things you are looking at must be measurable. These are called variables.
• That means, we have to be able to count or measure quantify the variables we are trying to connect.

Now look at the key words in the 4 hypothesis sentences above. How can we measure these different things?

Check this file for a few possible answers .

Part 2: Practice #1 (10 minutes)

In this short task, students apply their new found knowledge of the hypothesis sentence pattern. The task uses a famous video clip with Steve Jobs .

Step 1: Introduce video clip. It is a small part of a speech made by Steve Jobs at a university convocation.

Step 2: Students listen to the video and summarize the main idea in the form of a hypothesis sentence pattern.

Step 3: Play video 2-3 times.

Step 4: Students to work in pairs and create one hypothesis sentence that summarizes the speaker’s main idea.

Step 5: Review answers in class. 

Part 3: Practice #2 (10 minutes)

Another practice round where students summarize data by creating hypothesis sentences. The suggested teaching approach is a pair work fluency drill.

Step 1: Put students in pairs or small groups.

Step 2: Introduce task. Students look at an image for one minute. They write one sentence hypothesis sentence that summarizes the data.

Step 3: Show the first image as a group practice effort.

Step 4: Give students 1 to 2 minutes to study the image and write a hypothesis sentence with their partner.

Step 5: After time has passed, review answers in class. 

Step 6: Begin the drill. Show each image for 1 – 2 minutes, or enough time for students to think about, create and write down one hypothesis statement.

Step 7: After all images have been examined, review sentences on whiteboard with whole class.

Here are some images and data sets for the drill:

Check this file to few the graphs and show some  possible answers .

Part 4: World History Video Summary (20-40 minutes)

This video shows the history of Earth . 200 years of change in 4 minutes. It is a unique presentation that will help build your students’ vocabulary and listening skills. The video is also a good example of telling a great story with hypothesis sentences.

Step 1. Watch the video one time.

Step 2. Make notes and answer these questions with a partner.

• What is the variable for each axis on the graph?
• How is each variable counted or measured?
• Write one hypothesis sentence using the data from the video.

Step 3. Discuss answers with whole class.

Step 4. Write a paragraph or more to explain the cause and effect relationship in the hypothesis.

Optional Step: Vocabulary Preview

Depending on the needs of your class, it might be a good idea to preview some vocabulary before students watch the video. Here are some words and phrases critical to video comprehension.

• life expectancy
• income per person
• Middle East
• industrial revolution
• Great Depression
• to catch up
• inequalities

Enjoy the lesson. Cheers!

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3 thoughts on “writing hypothesis sentences”.

Great site!

Thank you for the video. I can understand it, but I can’t define or explain it in ratio form. Please define and answer your question for me, so I can better understand. Thank you again.

Really good explanation. I’ll try to use it during lessons. I like a lot creative lessons ant this is one of them.

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HOW TO WRITE A HYPOTHESIS

Writing a hypothesis

Frequently, when we hear the word ‘hypothesis’, we immediately think of an investigation in the form of a science experiment. This is not surprising, as science is the subject area where we are usually first introduced to the term.

However, the term hypothesis also applies to investigations and research in many diverse areas and branches of learning, leaving us wondering how to write a hypothesis in statistics and how to write a hypothesis in sociology alongside how to write a hypothesis in a lab report.

We can find hypotheses at work in areas as wide-ranging as history, psychology, technology, engineering, literature, design, and economics. With such a vast array of uses, hypothesis writing is an essential skill for our students to develop.

What Is a Hypothesis?

A hypothesis is a proposed or predicted answer to a question. The purpose of writing a hypothesis is to follow it up by testing that answer. This test can take the form of an investigation, experiment, or writing a research paper that will ideally prove or disprove the hypothesis’s prediction.

Despite this element of the unknown, a hypothesis is not the same thing as a guess. Though the hypothesis writer typically has some uncertainty, the creation of the hypothesis is generally based on some background knowledge and research of the topic. The writer believes in the likelihood of a specific outcome, but further investigation will be required to validate or falsify the claim made in their hypothesis.

In this regard, a hypothesis is more along the lines of an ‘educated guess’ that has been based on observation and/or background knowledge.

A hypothesis should:

• Make a prediction
• Provide reasons for that prediction
• Specifies a relationship between two or more variables
• Be testable
• Be falsifiable
• Be expressed simply and concisely
• Serves as the starting point for an investigation, an experiment, or another form of testing

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Hypothesis Examples for Students and Teachers

If students listen to classical music while studying, they will retain more information.

Mold growth is affected by the level of moisture in the air.

Students who sleep for longer at night retain more information at school.

Employees who work more than 40 hours per week show higher instances of clinical depression.

Time spent on social media is negatively correlated to the length of the average attention span.

People who spend time exercising regularly are less likely to develop a cardiovascular illness.

If people are shorter, then they are more likely to live longer.

What are Variables in a Hypothesis?

Variables are an essential aspect of any hypothesis. But what exactly do we mean by this term?

Variables are changeable factors or characteristics that may affect the outcome of an investigation. Things like age, weight, the height of participants, length of time, the difficulty of reading material, etc., could all be considered variables.

Usually, an investigation or experiment will focus on how different variables affect each other. So, it is vital to define the variables clearly if you are to measure the effect they have on each other accurately.

There are three main types of variables to consider in a hypothesis. These are:

• Independent Variables
• Dependent Variables

The Independent Variable

The independent variable is unaffected by any of the other variables in the hypothesis. We can think of the independent variable as the assumed cause .

The Dependent Variable

The dependent variable is affected by the other variables in the hypothesis. It is what is being tested or measured. We can think of the dependent variable as the assumed effect .

For example, let’s investigate the correlation between test scores across different age groups. The age groups will be the independent variable, and the test scores will be the dependent variable .

Now that we know what variables are let’s look at how they work in the various types of hypotheses.

Types of Hypotheses

There are many different types of hypotheses, and it is helpful to know the most common of these if the student selects the most suitable tool for their specific job.

The most frequently used types of hypotheses are:

The Simple Hypothesis

The complex hypothesis, the empirical hypothesis, the null hypothesis, the directional hypothesis, the non-directional hypothesis.

This straightforward hypothesis type predicts the relationship between an independent and dependent variable.

Example: Eating too much sugar causes weight gain.

This type of hypothesis is based on the relationship between multiple independent and/or dependent variables.

Example: Overeating sugar causes weight gain and poor cardiovascular health.

Also called a working hypothesis, an empirical hypothesis is tested through observation and experimentation. An empirical hypothesis is produced through investigation and trial and error. As a result, the empirical hypothesis may change its independent variables in the process.

Example: Exposure to sunlight helps lettuces grow faster.

This hypothesis states that there is no significant or meaningful relationship between specific variables.

Example: Exposure to sunlight does not affect the rate of a plant’s growth.

This type of hypothesis predicts the direction of an effect between variables, i.e., positive or negative.

Example: A high-quality education will result in a greater number of career opportunities.

Similar to the directional hypothesis, this type of hypothesis predicts the nature of the effect but not the direction that effect will go in.

Example: A high-quality education will affect the number of available career opportunities.

How to Write a Hypothesis : A STEP-BY-STEP GUIDE

• Ask a Question

The starting point for any hypothesis is asking a question. This is often called the research question . The research question is the student’s jumping-off point to developing their hypothesis. This question should be specific and answerable. The hypothesis will be the point where the research question is transformed into a declarative statement.

Ideally, the questions the students develop should be relational, i.e., they should look at how two or more variables relate to each other as described above. For example, what effect does sunlight have on the growth rate of lettuce?

• Research the Question

The research is an essential part of the process of developing a hypothesis. Students will need to examine the ideas and studies that are out there on the topic already. By examining the literature already out there on their topic, they can begin to refine their questions on the subject and begin to form predictions based on their studies.

Remember, a hypothesis can be defined as an ‘educated’ guess. This is the part of the process where the student educates themself on the subject before making their ‘guess.’

• Define Your Variables

By now, your students should be ready to form their preliminary hypotheses. To do this, they should first focus on defining their independent and dependent variables. Now may be an excellent opportunity to remind students that the independent variables are the only variables that they have complete control over, while dependent variables are what is tested or measured.

• Develop Your Preliminary Hypotheses

With variables defined, students can now work on a draft of their hypothesis. To do this, they can begin by examining their variables and the available data and then making a statement about the relationship between these variables. Students must brainstorm and reflect on what they expect to happen in their investigation before making a prediction upon which to base their hypothesis. It’s worth noting, too, that hypotheses are typically, though not exclusively, written in the present tense.

Students revisit the different types of hypotheses described earlier in this article. Students select three types of hypotheses and frame their preliminary hypotheses according to each criteria. Which works best? Which type is the least suitable for the student’s hypothesis?

• Finalize the Phrasing

By now, students will have made a decision on which type of hypothesis suits their needs best, and it will now be time to finalize the wording of their hypotheses. There are various ways that students can choose to frame their hypothesis, but below, we will examine the three most common ways.

The If/Then Phrasing

This is the most common type of hypothesis and perhaps the easiest to write for students. It follows a simple ‘ If x, then y ’ formula that makes a prediction that forms the basis of a subsequent investigation.

If I eat more calories, then I will gain weight.

Correlation Phrasing

Another way to phrase a hypothesis is to focus on the correlation between the variables. This typically takes the form of a statement that defines that relationship positively or negatively.

The more calories that are eaten beyond the daily recommended requirements, the greater the weight gain will be.

Comparison Phrasing

This form of phrasing is applicable when comparing two groups and focuses on the differences that the investigation is expected to reveal between those two groups.

Those who eat more calories will gain more weight than those who eat fewer calories.

Questions to ask during this process include:

• What tense is the hypothesis written in?
• Does the hypothesis contain both independent and dependent variables?
• Is the hypothesis framed using the if/then, correlation, or comparison framework (or other similar suitable structure)?
• Is the hypothesis worded clearly and concisely?
• Does the hypothesis make a prediction?
• Is the prediction specific?
• Is the hypothesis testable?
• Gather Data to Support/Disprove Your Hypothesis

If the purpose of a hypothesis is to provide a reason to pursue an investigation, then the student will need to gather related information together to fuel that investigation.

While, by definition, a hypothesis leans towards a specific outcome, the student shouldn’t worry if their investigations or experiments ultimately disprove their hypothesis. The hypothesis is the starting point; the destination is not preordained. This is the very essence of the scientific method. Students should trust the results of their investigation to speak for themselves. Either way, the outcome is valuable information.

TOP 10 TIPS FOR WRITING A STRONG HYPOTHESIS

• Begin by asking a clear and compelling question. Your hypothesis is a response to the inquiry you are eager to explore.
• Keep it simple and straightforward. Avoid using complex phrases or making multiple predictions in one hypothesis.
• Use the right format. A strong hypothesis is often written in the form of an “if-then” statement.
• Ensure that your hypothesis is testable. Your hypothesis should be something that can be verified through experimentation or observation.
• Stay objective. Your hypothesis should be based on facts and evidence, not personal opinions or prejudices.
• Examine different possibilities. Don’t limit yourself to just one hypothesis. Consider alternative explanations for your observations.
• Stay open to the possibility of being wrong. Your hypothesis is just a prediction, and it may not always be correct.
• Search for evidence to support your hypothesis. Investigate existing literature and gather data that supports your hypothesis.
• Make sure that your hypothesis is pertinent. Your hypothesis should be relevant to the question you are trying to investigate.
• Revise your hypothesis as necessary. If new evidence arises that contradicts your hypothesis, you may need to adjust it accordingly.

HYPOTHESIS TEACHING STRATEGIES AND ACTIVITIES

When teaching young scientists and writers, it’s essential to remember that the process of formulating a hypothesis is not always straightforward. It’s easy to make mistakes along the way, but with a bit of guidance, you can ensure your students avoid some of the most common pitfalls like these.

• Don’t let your students be too vague. Remind them that when formulating a hypothesis, it’s essential to be specific and avoid using overly general language. Make sure their hypothesis is clear and easy to understand.
• Being swayed by personal biases will impact their hypothesis negatively. It’s important to stay objective when formulating a hypothesis, so avoid letting personal biases or opinions get in the way.
• Not starting with a clear question is the number one stumbling block for students, so before forming a hypothesis, you need to reinforce the need for a clear understanding of the question they’re trying to answer. Start with a question that is specific and relevant.

Hypothesis Warmup Activity: First, organize students into small working groups of four or five. Then, set each group to collect a list of hypotheses. They can find these by searching on the Internet or finding examples in textbooks . When students have gathered together a suitable list of hypotheses, have them identify the independent and dependent variables in each case. They can underline each of these in different colors.

It may be helpful for students to examine each hypothesis to identify the ‘cause’ elements and the ‘effect’ elements. When students have finished, they can present their findings to the class.

Task 1: Set your students the task of coming up with an investigation-worthy question on a topic that interests them. This activity works particularly well for groups.

Task 2: Students search for existing information and theories on their topic on the Internet or in the library. They should take notes where necessary and begin to form an assumption or prediction based on their reading and research that they can investigate further.

Task 3: When working with a talking partner, can students identify which of their partner’s independent and dependent variables? If not, then one partner will need to revisit the definitions for the two types of variables as outlined earlier.

Task 4: Organize students into smaller groups and task them with presenting their hypotheses to each other. Students can then provide feedback before the final wording of each hypothesis is finalized.

Perhaps due to their short length, learning how to create a well-written hypothesis is not typically afforded much time in the curriculum.

However, though they are brief in length, they are complex enough to warrant focused learning and practice in class, particularly given their importance across many curriculum areas.

Learning how to write a hypothesis works well as a standalone writing skill. It can also form part of a more comprehensive academic or scientific writing study that focuses on how to write a research question, develop a theory, etc.

As with any text type, practice improves performance. By following the processes outlined above, students will be well on their way to writing their own hypotheses competently in no time.

• How To Write A Hypothesis

How to Write a Hypothesis: Types and Tips to Remember

Many people might not know what a hypothesis is, the purpose of a hypothesis or where a hypothesis is needed. A hypothesis is a statement that explains the research’s predictions and the reasons behind the research. It is an “educated guess” of the final result of the research problem and is written for an academic research paper. A good hypothesis is carefully stated as a key aspect of the scientific method, yet even the simplest ones can be difficult to explain.

If you are unaware of the process of writing a hypothesis, we are here to help you with all your queries. Read the article and learn how to write a hypothesis for your academic paper/thesis.

Table of Contents

What is a hypothesis.

• Simple Hypothesis
• Complex Hypothesis
• Null Hypothesis
• Alternative Hypothesis
• Logical Hypothesis
• Empirical Hypothesis
• Statistical Hypothesis

Writing a Good Hypothesis – Points to Remember

• How to Write a Hypothesis

Frequently Asked Questions on How to Write a Hypothesis

A hypothesis is prepared in the early stages of a research project. Based on the preliminary research observations, a hypothesis is framed. It is the prediction of the end result of the research problem. For example, suppose you have observed that the plants grow up better with regular watering. In that case, your hypothesis can be “Plants grow better with regular watering”. Once you have got your hypothesis, you can begin the experiments required to support and prove it.

A hypothesis must include variables. It can be some events, objects or concepts which are to be observed and tested for your research experiments. There are two kinds of variables – dependent variables and independent variables. The independent variables are the ones which can be modified in the experiment, and the dependent variables are the ones which can only be observed.

Hypotheses are a crucial part of the research paper since they influence the direction and arrangement of the research methods. The readers will want to know if the hypothesis was proven right or wrong, and therefore it must be mentioned clearly in the introduction or the abstract of the paper.

Types of Hypotheses

Depending on the nature of the research and the findings, the hypothesis can be categorised into one or more of the seven major categories.

1. Simple Hypothesis

A simple hypothesis states the relationship between the two variables (dependent and independent variables).

2. Complex Hypothesis

A complex hypothesis entails the existence of a relationship between two or more variables. It can be two dependent variables and one independent variable or vice versa.

3. Null Hypothesis

A null hypothesis is a statement that states that the variables have no relationship.

4. Alternative Hypothesis

The null hypothesis is the polar opposite of the alternative hypothesis. It states that the two variables under study have a link (one variable has an effect on the other).

5. Logical Hypothesis

In the absence of verifiable proof, a logical hypothesis indicates a relationship between variables. Assertions are based on inference or logic rather than evidence.

6. Empirical Hypothesis

An empirical hypothesis, often known as a “working hypothesis,” is one that is being researched right now. Empirical hypotheses, unlike logical assumptions, are supported by evidence.

7. Statistical Hypothesis

When you test a sample of a population and then use the collected statistical evidence to draw conclusions about the full population, you’ve generated a statistical hypothesis. You test a section of it and then make an educated guess about the rest based on the results.

A good hypothesis is written following the same format and guidelines. To write a good hypothesis, the below-mentioned information has to be added.

Causes and Effects: A hypothesis always includes a cause-and-effect relationship where one variable causes another to change or not change, depending on the type of hypothesis.

Measurable Prediction: Other than logical hypotheses, most hypotheses are designed to be tested. Before you commit to any hypothesis, make sure that it is experimented. Select a testable hypothesis involving an independent variable over which you can have complete control.

Dependent and Independent Variables: You can define the type of variables of your research for the readers.

Language used in a Hypothesis: Make sure to write the hypothesis in simple and clear language.

Adhere to Ethics: Before conducting your research, keep an eye on what you are experimenting with. Those hypotheses which are objectionable, questionable or taboo can be avoided unless they are absolutely necessary.

How to Write a Hypothesis?

A good hypothesis can be written in the following six steps.

Asking a Question

Arousing curiosity in the minds of the readers can be a good way to start a hypothesis. It would make the readers think about the topic critically.

Conducting a Preliminary Research

Before writing the hypothesis, it is essential to get background information regarding the topic. The preliminary research can be done through various web searches, reading books, etc.

Defining the Variables

After you have decided on your hypothesis, you can now decide on your variables. Keep in mind that the independent variables are the ones over which you have complete control and accordingly decide the limits of your hypothesis.

Writing the Hypothesis in the “if-then” Statement

While writing a hypothesis, keep in mind that it must be written in an “if-then” format statement which is a reliable method of expressing the causes and effects. A simple example would be, “If we water the plants daily, then they might grow really well.”

Collection of Adequate Data to Back the Hypothesis

A hypothesis is written to reach the conclusion of the research. After writing the hypothesis, the experiments can be conducted. See to it that you collect the adequate data needed to support the hypothesis.

Writing with Confidence

After you have collected enough data, you can start writing the hypothesis. Make sure you write confidently, without any errors. It would be good to get your writing counter-checked by an expert if you are not confident about it.

What is a hypothesis?

A hypothesis is a statement that explains the research’s predictions and the reasons behind the research. It is written based on various observations.

Why is a hypothesis important?

A hypothesis is important in an academic paper because it explains the result of the research problem. It will help the researcher, as well as the audience, to stay focused and not deviate from the main idea.

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5.2 - writing hypotheses.

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

• At this point we can write hypotheses for a single mean (\(\mu\)), paired means(\(\mu_d\)), a single proportion (\(p\)), the difference between two independent means (\(\mu_1-\mu_2\)), the difference between two proportions (\(p_1-p_2\)), a simple linear regression slope (\(\beta\)), and a correlation (\(\rho\)). 
• The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
• The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., \(\mu_0\) and \(p_0\)). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., \(p\) and \(\mu\)).  The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

Statistics Made Easy

How to Write Hypothesis Test Conclusions (With Examples)

A   hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

• Null Hypothesis (H 0 ): The sample data occurs purely from chance.
• Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

• Whether we reject or fail to reject the null hypothesis.
• The significance level.
• A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level.   There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

• H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
• H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.

He performs a hypothesis test at a 10% significance level using the following hypotheses:

• H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
• H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level.   There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

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Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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8.4: Hypothesis Test Examples for Proportions

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• In a hypothesis test problem, you may see words such as "the level of significance is 1%." The "1%" is the preconceived or preset \(\alpha\).
• The statistician setting up the hypothesis test selects the value of α to use before collecting the sample data.
• If no level of significance is given, a common standard to use is \(\alpha = 0.05\).
• When you calculate the \(p\)-value and draw the picture, the \(p\)-value is the area in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two tailed.
• The alternative hypothesis, \(H_{a}\), tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test.
• \(H_{a}\) never has a symbol that contains an equal sign.
• Thinking about the meaning of the \(p\)-value: A data analyst (and anyone else) should have more confidence that he made the correct decision to reject the null hypothesis with a smaller \(p\)-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha. Similarly, for a large p -value such as 0.4, as opposed to a \(p\)-value of 0.056 (\(\alpha = 0.05\) is less than either number), a data analyst should have more confidence that she made the correct decision in not rejecting the null hypothesis. This makes the data analyst use judgment rather than mindlessly applying rules.

Full Hypothesis Test Examples

Example \(\PageIndex{7}\)

Joon believes that 50% of first-time brides in the United States are younger than their grooms. She performs a hypothesis test to determine if the percentage is the same or different from 50% . Joon samples 100 first-time brides and 53 reply that they are younger than their grooms. For the hypothesis test, she uses a 1% level of significance.

Set up the hypothesis test:

The 1% level of significance means that α = 0.01. This is a test of a single population proportion .

\(H_{0}: p = 0.50\)  \(H_{a}: p \neq 0.50\)

The words "is the same or different from" tell you this is a two-tailed test.

Calculate the distribution needed:

Random variable: \(P′ =\) the percent of of first-time brides who are younger than their grooms.

Distribution for the test: The problem contains no mention of a mean. The information is given in terms of percentages. Use the distribution for P′ , the estimated proportion.

\[P' - N\left(p, \sqrt{\frac{p-q}{n}}\right)\nonumber \]

\[P' - N\left(0.5, \sqrt{\frac{0.5-0.5}{100}}\right)\nonumber \]

where \(p = 0.50, q = 1−p = 0.50\), and \(n = 100\)

Calculate the p -value using the normal distribution for proportions:

\[p\text{-value} = P(p′ < 0.47 or p′ > 0.53) = 0.5485\nonumber \]

where \[x = 53, p' = \frac{x}{n} = \frac{53}{100} = 0.53\nonumber \].

Interpretation of the \(p\text{-value})\: If the null hypothesis is true, there is 0.5485 probability (54.85%) that the sample (estimated) proportion \(p'\) is 0.53 or more OR 0.47 or less (see the graph in Figure).

\(\mu = p = 0.50\) comes from \(H_{0}\), the null hypothesis.

\(p′ = 0.53\). Since the curve is symmetrical and the test is two-tailed, the \(p′\) for the left tail is equal to \(0.50 – 0.03 = 0.47\) where \(\mu = p = 0.50\). (0.03 is the difference between 0.53 and 0.50.)

Compare \(\alpha\) and the \(p\text{-value}\):

Since \(\alpha = 0.01\) and \(p\text{-value} = 0.5485\). \(\alpha < p\text{-value}\).

Make a decision: Since \(\alpha < p\text{-value}\), you cannot reject \(H_{0}\).

Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of first-time brides who are younger than their grooms is different from 50%.

The \(p\text{-value}\) can easily be calculated.

Press STAT and arrow over to TESTS . Press 5:1-PropZTest . Enter .5 for \(p_{0}\), 53 for \(x\) and 100 for \(n\). Arrow down to Prop and arrow to not equals \(p_{0}\). Press ENTER . Arrow down to Calculate and press ENTER . The calculator calculates the \(p\text{-value}\) (\(p = 0.5485\)) and the test statistic (\(z\)-score). Prop not equals .5 is the alternate hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate ). Press ENTER . A shaded graph appears with \(\(z\) = 0.6\) (test statistic) and \(p = 0.5485\) (\(p\text{-value}\)). Make sure when you use Draw that no other equations are highlighted in \(Y =\) and the plots are turned off.

The Type I and Type II errors are as follows:

The Type I error is to conclude that the proportion of first-time brides who are younger than their grooms is different from 50% when, in fact, the proportion is actually 50%. (Reject the null hypothesis when the null hypothesis is true).

The Type II error is there is not enough evidence to conclude that the proportion of first time brides who are younger than their grooms differs from 50% when, in fact, the proportion does differ from 50%. (Do not reject the null hypothesis when the null hypothesis is false.)

Exercise \(\PageIndex{7}\)

A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.

First, determine what type of test this is, set up the hypothesis test, find the \(p\text{-value}\), sketch the graph, and state your conclusion.

Since the problem is about percentages, this is a test of single population proportions.

• \(H_{0} : p = 0.85\)
• \(H_{a}: p \neq 0.85\)
• \(p = 0.7554\)

Because \(p > \alpha\), we fail to reject the null hypothesis. There is not sufficient evidence to suggest that the proportion of students that want to go to the zoo is not 85%.

Example \(\PageIndex{8}\)

Suppose a consumer group suspects that the proportion of households that have three cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%. Before they start a big advertising campaign, they conduct a hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Set up the Hypothesis Test:

\(H_{0}: p = 0.30, H_{a}: p \neq 0.30\)

Determine the distribution needed:

The random variable is \(P′ =\) proportion of households that have three cell phones.

The distribution for the hypothesis test is \(P' - N\left(0.30, \sqrt{\frac{(0.30 \cdot 0.70)}{150}}\right)\)

Exercise 9.6.8.2

a. The value that helps determine the \(p\text{-value}\) is \(p′\). Calculate \(p′\).

a. \(p' = \frac{x}{n}\) where \(x\) is the number of successes and \(n\) is the total number in the sample.

\(x = 43, n = 150\)

\(p′ = 43150\)

Exercise 9.6.8.3

b. What is a success for this problem?

b. A success is having three cell phones in a household.

Exercise 9.6.8.4

c. What is the level of significance?

c. The level of significance is the preset \(\alpha\). Since \(\alpha\) is not given, assume that \(\alpha = 0.05\).

Exercise 9.6.8.5

d. Draw the graph for this problem. Draw the horizontal axis. Label and shade appropriately.

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

d. \(p\text{-value} = 0.7216\)

Exercise 9.6.8.6

e. Make a decision. _____________(Reject/Do not reject) \(H_{0}\) because____________.

e. Assuming that \(\alpha = 0.05, \alpha < p\text{-value}\). The decision is do not reject \(H_{0}\) because there is not sufficient evidence to conclude that the proportion of households that have three cell phones is not 30%.

Exercise \(\PageIndex{8}\)

Marketers believe that 92% of adults in the United States own a cell phone. A cell phone manufacturer believes that number is actually lower. 200 American adults are surveyed, of which, 174 report having cell phones. Use a 5% level of significance. State the null and alternative hypothesis, find the p -value, state your conclusion, and identify the Type I and Type II errors.

• \(H_{0}: p = 0.92\)
• \(H_{a}: p < 0.92\)
• \(p\text{-value} = 0.0046\)

Because \(p < 0.05\), we reject the null hypothesis. There is sufficient evidence to conclude that fewer than 92% of American adults own cell phones.

• Type I Error: To conclude that fewer than 92% of American adults own cell phones when, in fact, 92% of American adults do own cell phones (reject the null hypothesis when the null hypothesis is true).
• Type II Error: To conclude that 92% of American adults own cell phones when, in fact, fewer than 92% of American adults own cell phones (do not reject the null hypothesis when the null hypothesis is false).

The next example is a poem written by a statistics student named Nicole Hart. The solution to the problem follows the poem. Notice that the hypothesis test is for a single population proportion. This means that the null and alternate hypotheses use the parameter \(p\). The distribution for the test is normal. The estimated proportion \(p′\) is the proportion of fleas killed to the total fleas found on Fido. This is sample information. The problem gives a preconceived \(\alpha = 0.01\), for comparison, and a 95% confidence interval computation. The poem is clever and humorous, so please enjoy it!

Example \(\PageIndex{9}\)

My dog has so many fleas,

They do not come off with ease. As for shampoo, I have tried many types Even one called Bubble Hype, Which only killed 25% of the fleas, Unfortunately I was not pleased.

I've used all kinds of soap, Until I had given up hope Until one day I saw An ad that put me in awe.

A shampoo used for dogs Called GOOD ENOUGH to Clean a Hog Guaranteed to kill more fleas.

I gave Fido a bath And after doing the math His number of fleas Started dropping by 3's! Before his shampoo I counted 42.

At the end of his bath, I redid the math And the new shampoo had killed 17 fleas. So now I was pleased.

Now it is time for you to have some fun With the level of significance being .01, You must help me figure out

Use the new shampoo or go without?

\(H_{0}: p \leq 0.25\)   \(H_{a}: p > 0.25\)

In words, CLEARLY state what your random variable \(\bar{X}\) or \(P′\) represents.

\(P′ =\) The proportion of fleas that are killed by the new shampoo

State the distribution to use for the test.

\[N\left(0.25, \sqrt{\frac{(0.25){1-0.25}}{42}}\right)\nonumber \]

Test Statistic: \(z = 2.3163\)

Calculate the \(p\text{-value}\) using the normal distribution for proportions:

\[p\text{-value} = 0.0103\nonumber \]

In one to two complete sentences, explain what the p -value means for this problem.

If the null hypothesis is true (the proportion is 0.25), then there is a 0.0103 probability that the sample (estimated) proportion is 0.4048 \(\left(\frac{17}{42}\right)\) or more.

Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and shade the region(s) corresponding to the \(p\text{-value}\).

Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

Conclusion: At the 1% level of significance, the sample data do not show sufficient evidence that the percentage of fleas that are killed by the new shampoo is more than 25%.

Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval.

Confidence Interval: (0.26,0.55) We are 95% confident that the true population proportion p of fleas that are killed by the new shampoo is between 26% and 55%.

This test result is not very definitive since the \(p\text{-value}\) is very close to alpha. In reality, one would probably do more tests by giving the dog another bath after the fleas have had a chance to return.

Example \(\PageIndex{11}\)

In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue, use a 0.005 significance level. Explain why the significance level should be so low in terms of a Type I error.

We will follow the four-step process.

• \(H_{0}: p \leq 0.00034\)
• \(H_{a}: p > 0.00034\)

If we commit a Type I error, we are essentially accepting a false claim. Since the claim describes cancer-causing environments, we want to minimize the chances of incorrectly identifying causes of cancer.

• We will be testing a sample proportion with \(x = 172\) and \(n = 420,019\). The sample is sufficiently large because we have \(np = 420,019(0.00034) = 142.8\), \(nq = 420,019(0.99966) = 419,876.2\), two independent outcomes, and a fixed probability of success \(p = 0.00034\). Thus we will be able to generalize our results to the population.

Figure 9.6.11.

Figure 9.6.12.

• Since the \(p\text{-value} = 0.0073\) is greater than our alpha value \(= 0.005\), we cannot reject the null. Therefore, we conclude that there is not enough evidence to support the claim of higher brain cancer rates for the cell phone users.

Example \(\PageIndex{12}\)

According to the US Census there are approximately 268,608,618 residents aged 12 and older. Statistics from the Rape, Abuse, and Incest National Network indicate that, on average, 207,754 rapes occur each year (male and female) for persons aged 12 and older. This translates into a percentage of sexual assaults of 0.078%. In Daviess County, KY, there were reported 11 rapes for a population of 37,937. Conduct an appropriate hypothesis test to determine if there is a statistically significant difference between the local sexual assault percentage and the national sexual assault percentage. Use a significance level of 0.01.

We will follow the four-step plan.

• We need to test whether the proportion of sexual assaults in Daviess County, KY is significantly different from the national average.
• \(H_{0}: p = 0.00078\)
• \(H_{a}: p \neq 0.00078\)

Figure 9.6.13.

Figure 9.6.14.

• Since the \(p\text{-value}\), \(p = 0.00063\), is less than the alpha level of 0.01, the sample data indicates that we should reject the null hypothesis. In conclusion, the sample data support the claim that the proportion of sexual assaults in Daviess County, Kentucky is different from the national average proportion.

The hypothesis test itself has an established process. This can be summarized as follows:

• Determine \(H_{0}\) and \(H_{a}\). Remember, they are contradictory.
• Determine the random variable.
• Determine the distribution for the test.
• Draw a graph, calculate the test statistic, and use the test statistic to calculate the \(p\text{-value}\). (A z -score and a t -score are examples of test statistics.)
• Compare the preconceived α with the p -value, make a decision (reject or do not reject H 0 ), and write a clear conclusion using English sentences.

Notice that in performing the hypothesis test, you use \(\alpha\) and not \(\beta\). \(\beta\) is needed to help determine the sample size of the data that is used in calculating the \(p\text{-value}\). Remember that the quantity \(1 – \beta\) is called the Power of the Test . A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same.If the power is low, the null hypothesis might not be rejected when it should be.

• Data from Amit Schitai. Director of Instructional Technology and Distance Learning. LBCC.
• Data from Bloomberg Businessweek . Available online at http://www.businessweek.com/news/2011- 09-15/nyc-smoking-rate-falls-to-record-low-of-14-bloomberg-says.html.
• Data from energy.gov. Available online at http://energy.gov (accessed June 27. 2013).
• Data from Gallup®. Available online at www.gallup.com (accessed June 27, 2013).
• Data from Growing by Degrees by Allen and Seaman.
• Data from La Leche League International. Available online at www.lalecheleague.org/Law/BAFeb01.html.
• Data from the American Automobile Association. Available online at www.aaa.com (accessed June 27, 2013).
• Data from the American Library Association. Available online at www.ala.org (accessed June 27, 2013).
• Data from the Bureau of Labor Statistics. Available online at http://www.bls.gov/oes/current/oes291111.htm .
• Data from the Centers for Disease Control and Prevention. Available online at www.cdc.gov (accessed June 27, 2013)
• Data from the U.S. Census Bureau, available online at quickfacts.census.gov/qfd/states/00000.html (accessed June 27, 2013).
• Data from the United States Census Bureau. Available online at www.census.gov/hhes/socdemo/language/.
• Data from Toastmasters International. Available online at http://toastmasters.org/artisan/deta...eID=429&Page=1 .
• Data from Weather Underground. Available online at www.wunderground.com (accessed June 27, 2013).
• Federal Bureau of Investigations. “Uniform Crime Reports and Index of Crime in Daviess in the State of Kentucky enforced by Daviess County from 1985 to 2005.” Available online at http://www.disastercenter.com/kentucky/crime/3868.htm (accessed June 27, 2013).
• “Foothill-De Anza Community College District.” De Anza College, Winter 2006. Available online at research.fhda.edu/factbook/DA...t_da_2006w.pdf.
• Johansen, C., J. Boice, Jr., J. McLaughlin, J. Olsen. “Cellular Telephones and Cancer—a Nationwide Cohort Study in Denmark.” Institute of Cancer Epidemiology and the Danish Cancer Society, 93(3):203-7. Available online at http://www.ncbi.nlm.nih.gov/pubmed/11158188 (accessed June 27, 2013).
• Rape, Abuse & Incest National Network. “How often does sexual assault occur?” RAINN, 2009. Available online at www.rainn.org/get-information...sexual-assault (accessed June 27, 2013).

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

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The Science of Siblings

Gay people often have older brothers. why and does it matter.

Selena Simmons-Duffin

Credit: Lily Padula for NPR

The Science of Siblings is a new series exploring the ways our siblings can influence us, from our money and our mental health all the way down to our very molecules. We'll be sharing these stories over the next several weeks.

This is something I learned years ago through gay bar chatter: Gay people are often the youngest kids in their families. I liked the idea right away — as a gay youngest sibling, it made me feel like there was a statistical order to things and I fit neatly into that order.

When I started to report on the science behind it, I learned it's true: There is a well-documented correlation between having older siblings (older brothers, specifically) and a person's chance of being gay. But parts of the story also struck me as strange and dark. I thought of We the Animals , Justin Torres' haunting semi-autobiographical novel about three brothers — the youngest of whom is queer — growing up in New York state. So I called Torres to get his take on the idea.

Torres' first reaction was to find it considerably less appealing than I did. This makes sense — his latest novel, Blackouts , won a National Book Award last year, and it grapples with the sinister history of how scientists have studied sexuality. "My novel is interested in the pre-Kinsey sexology studies, specifically this one called Sex Variants ," he told me. "It's really informed by eugenics. They were looking for the cause of homosexuality in the body in order to treat it or cure it or get rid of it."

That's why, when he saw my inquiry about a statistical finding that connects sexuality and birth order, he was wary. "To be frank, I find these kinds of studies that're looking for something rooted in the body to explain sexuality to be kind of bunk. I think they rely on a really binary understanding of sexuality itself," he said.

"That's fair," I conceded. But this connection between queerness and older brothers has been found so many times in so many places that one researcher told me it's "a kind of truth" in the science of sexuality.

Rooted in a dark past

The first research on this topic did indeed begin in the 1940s and '50s, during that era of investigations into what causes homosexuality, to be able to cure it. At the time, the queer people whom scientists were studying were living in a world where this facet of their identity was dangerous. Plus, the studies themselves didn't find much, says Jan Kabátek , a senior research fellow at the University of Melbourne.

"Most of it fell flat," he told me. "But there is an exception to this, and that is the finding that men, specifically, who exhibit attraction to the same sex are likely to have more older brothers than other types of siblings."

In the 1990s, this was dubbed the "fraternal birth order effect." In the years since, it has been found again and again, all over the world.

"This pattern has been documented around Canada and the United States, but it goes well beyond that," says Scott Semenyna , a psychology professor at Stetson University. "There's been now many confirmations that this pattern exists in countries like Samoa. It exists in southern Mexico. It exists in places like Turkey and Brazil."

Huge study, consistent findings

An impressive recent study established that this pattern held up in an analysis of a huge sample — over 9 million people from the Netherlands. It confirmed all those earlier studies and added a twist.

"Interestingly enough — and this is quite different from what has been done before — we also showed that the same association manifests for women," explains Kabátek, one of the study's authors. Women who were in same-sex marriages were also more likely to have older brothers than other types of siblings.

At baseline, the chance that someone will be gay is pretty small. "Somewhere around 2 to 3% — we can call it 2% just for the sake of simplicity," Semenyna says. "The fraternal birth order effect shows that you're going to run into about a 33% increase in the probability of, like, male same-sex attraction for every older brother that you have."

The effect is cumulative: The more older brothers someone has, the bigger it is. If you have one older brother, your probability of being gay nudges up to about 2.6%. "And then that probability would increase another 33% if there was a second older brother, to about 3.5%," Semenyna says.

If you have five older brothers, your chance of being gay is about 8% — so, four times the baseline probability.

The author, Selena Simmons-Duffin, at age 3, with her brother, David Simmons-Duffin, at age 5. The Simmons-Duffin family hide caption

The author, Selena Simmons-Duffin, at age 3, with her brother, David Simmons-Duffin, at age 5.

Still, even 8% is pretty small. "The vast majority of people who have a lot of older brothers are still going to come out opposite-sex attracted," Semenyna says. Also, plenty of gay people have no brothers at all, or they're the oldest in their families. Having older brothers is definitely not the only influence on a person's sexuality.

"But just the fact that we are observing effects that are so strong, relatively speaking, implies that there's a good chance that there is, at least partially, some biological mechanism that is driving these associations," Kabátek says.

A hypothesis, but no definitive mechanism

For decades, the leading candidate for that biological mechanism has been the "maternal immune hypothesis," Semenyna explains. "The basic version of this hypothesis is that when a male fetus is developing, the Y chromosome of the male produces proteins that are going to be recognized as foreign by the mother's immune system and it forms somewhat of an immune response to those proteins."

That immune response has some effect on the development of subsequent male fetuses, Semenyna says. The plausibility of this hypothesis was bolstered by a 2017 study that found "that mothers of gay sons have more of these antibodies that target these male-specific proteins than mothers of sons who are not gay or mothers who have no sons whatsoever," he says.

But now that Kabátek's study of the Dutch population has found that this pattern was present among women in same-sex marriages as well, there are new questions about whether this hypothesis is correct.

"One option is that the immune hypothesis works for both men and women," Kabátek says. "Of course, there can be also other explanations. It's for prospective research to make this clearer."

Fun to think about, but concerning too

In a way, I tell Justin Torres, this effect seems simple and fun to me. It's a concrete statistical finding, documented all over the world, and there's an intriguing hypothesis about why it may happen biologically. But darker undercurrents in all of it worry me, like raising a dangerous idea that becoming gay in the womb is the only version of gayness that is real — or a repackaged version of the old idea that mothers are to "blame."

"It is the undercurrents that worry me immensely," he responds. "I remember when I was a kid — I have this memory of watching daytime television. I must have been staying home from school sick in the late '80s or early '90s. The host polled the audience and said, 'If there was a test [during pregnancy] and you could know if your child was gay, would you abort?' I remember being so horrified and disturbed watching all those hands go up in the audience — just feeling so hated. At that young age, I knew this thing about myself, even if I wasn't ready to admit it."

Even if tolerance for queer people in American society has grown a lot since then, he says, "I think that tolerance waxes and wanes, and I worry about that line of thinking."

At the same time, he agrees that the idea of a connection with gay people being the youngest kids in their families is kind of hilarious. "One thing that pops into my mind is, like, maybe if you're just surrounded by a lot of men, you either choose or don't choose men, right?" he laughs.

Essentially, in his view, it's fun to think about, but probably not deeper than that.

"As a humanist, I just don't know why we need to look for explanations for something as complex and joyous and weird as sexuality," Torres says.

Then again, scientists are unlikely to be able to resist that mysterious, weird complexity. Even if the joy and self-expression and community and so many other parts of queerness and sexuality will always be more than statistics can explain.

More from the Science of Siblings series:

• A gunman stole his twin from him. This is what he's learned about grieving a sibling
• In the womb, a brother's hormones can shape a sister's future
• These identical twins both grew up with autism, but took very different paths
• Science of Siblings
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• homosexuality

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Biden pardons 11 people and shortens the sentences of 5 others convicted of non-violent drug crimes

President Joe Biden speaks before signing a $95 billion Ukraine aid package that also includes support for Israel, Taiwan, and other allies, in the State Dining Room of the White House, Wednesday, April 24, 2024, in Washington. (AP Photo/Evan Vucci)

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WASHINGTON (AP) — President Joe Biden has granted clemency to 16 people who were convicted of non-violent drug crimes, issuing pardons to 11 men and women and commuting the sentences of five other people in the latest use of his clemency power to address racial disparities in the justice system.

Biden said in a statement Wednesday that April is Second Chance Month and that many of the individuals getting clemency had received “disproportionately longer” sentences than they would have under current law.

The Democratic president is campaigning for reelection in November and is grappling with how to boost support from communities of color that heavily supported him over Republican Donald Trump in the 2020 election. The two rivals are headed for a likely rematch in November.

“Like my other clemency actions, these pardons and commutations reflect my overarching commitment to addressing racial disparities and improving public safety,” Biden said.

Biden said those receiving pardons had shown a commitment to bettering their lives and doing good in their communities. He said those who had their sentences commuted, or shortened, had shown they were worthy of forgiveness and the chance to build a future outside of prison.

The president issued his most recent pardons in December 2023 to thousands of people who were convicted of the use and simple possession of marijuana on federal lands and in the District of Columbia.

An Associated Press analysis of Justice Department data shows that Biden has granted 129 commutations, more than any predecessor in their first term, dating to Richard Nixon. Nixon issued the most pardons at 691.

A pardon is an expression of forgiveness by the president, commonly granted to recognize that a person convicted of a crime has accepted responsibility for their actions. A pardon doesn’t mean the person is considered innocent, but does restore some rights, such as voting, that are lost upon conviction. A commutation only reduces a sentence but does not affect a conviction.

Iran's judiciary confirms rapper Toomaj Salehi death sentence

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At least 13 palestinians killed in israeli strikes on rafah, medical officials say.

Israeli air strikes on three houses in the southern Gaza city of Rafah killed 13 people and wounded many others, medics said on Monday.

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Start-Up Founder Sentenced to 18 Months in Prison for Fraud

Manish Lachwani, who founded the software start-up HeadSpin, is the latest tech entrepreneur to face time in prison in recent years.

By Erin Griffith

Reporting from San Francisco

Another start-up founder is going to prison for overstating his company’s performance to investors.

Manish Lachwani, who last year pleaded guilty to three counts of defrauding investors at his software start-up, HeadSpin, was sentenced to one and a half years in prison on Friday. He will also pay a fine of $1 million.

Government prosecutors said Mr. Lachwani, 48, deceived investors by inflating HeadSpin’s revenue nearly fourfold, making false claims about its customers and creating fake invoices to cover it up. His misrepresentations allowed him to raise $117 million in funding from top investment firms, valuing his start-up at $1.1 billion.

When HeadSpin’s board members found out about the behavior in 2020, they pushed Mr. Lachwani to resign and slashed the company’s valuation by two-thirds.

Mr. Lachwani is at least the fourth start-up founder in recent years to face serious consequences after taking Silicon Valley’s culture of hype too far. Other founders currently in prison for fraud include Sam Bankman-Fried of the cryptocurrency exchange FTX and Elizabeth Holmes and Ramesh Balwani of the blood testing start-up Theranos.

Trevor Milton, a founder of the electric vehicle company Nikola, was sentenced to prison in December for fraud. Michael Rothenberg, a venture capital investor who was recently convicted of 12 counts of fraud and money laundering, is set to be sentenced in June. And Changpeng Zhao, who founded the cryptocurrency exchange Binance and pleaded guilty to money laundering last year, is scheduled to be sentenced later this month.

Carlos Watson, the founder of the digital media outlet Ozy Media, and Charlie Javice, founder of the financial aid start-up Frank, have pleaded not guilty to fraud charges and face trials later this year.

Past generations of start-up founders rarely faced lasting consequences for their exaggerations. But the last decade’s low interest rates led to growing sums being poured into tech start-ups . Some founders used that environment to stretch the truth about what their technology could do or how their business performed.

The government has stepped up its investigations into such situations. The Justice Department said last month that its fraud division tried more than 100 white-collar crime cases over the last two years, which was a record. It also announced plans to beef up its program to pay whistle-blowers.

At Mr. Lachwani’s sentencing on Friday, his lawyer, John Hemann, argued for a lower sentence because — unlike other start-up frauds — HeadSpin’s business was a success and investors did not lose money.

“He wasn’t making up a product,” Mr. Hemann said of Mr. Lachwani. “He wasn’t selling snake oil.”

Judge Charles Breyer of California’s Northern District court said success was not a panacea for fraud. Silicon Valley’s tech founders and executives need to know that exaggerating to investors will result in incarceration, no matter how successful they are, he said.

“If you win, there are no serious consequences — that simply can’t be the law,” he said.

Addressing the judge, Mr. Lachwani broke down in tears several times. He apologized to the investors he misled and spoke of HeadSpin’s success. “HeadSpin just got very big, very fast,” he said.

Other government agencies are also investigating founders. On Wednesday, the Consumer Financial Protection Bureau accused Austin Allred, founder of BloomTech, a coding school that let students pay tuition by promising a portion of their future income, of violating the law by making false claims to customers.

In one claim, Mr. Allred said a “cohort” of BloomTech’s students had a 100 percent job placement rate, but the “cohort” consisted of one student, the agency said. The C.F.P.B fined BloomTech $164,000 and barred it from making loans.

Erin Griffith covers tech companies, start-ups and the culture of Silicon Valley from San Francisco. More about Erin Griffith

A Guide to Digital Safety

A few simple changes can go a long way toward protecting yourself and your information online..

A data breach into your health information  can leave you feeling helpless. But there are steps you can take to limit the potential harm.

Don’t know where to start? These easy-to-follow tips  and best practices  will keep you safe with minimal effort.

Your email address has become a digital bread crumb that companies can use to link your activity across sites. Here’s how you can limit this .

Protect your most sensitive accounts by creating unique passwords and adding extra layers of verification .

There are stronger methods of two-factor authentication than text messages. Here are the pros and cons of each .

Do you store photos, videos and important documents in the cloud? Make sure you keep a copy of what you hold most dear .

Browser extensions are free add-ons that you can use to slow down or stop data collection. Here are a few to try.