examples of a null and alternative hypothesis

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Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

Null hypothesis (H 0 ): There’s no effect in the population .
Alternative hypothesis (H A ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, differences between null and alternative hypotheses, how to write null and alternative hypotheses, frequently asked questions about null and alternative hypotheses.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”, the null hypothesis (H 0 ) answers “No, there’s no effect in the population.” On the other hand, the alternative hypothesis (H A ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample.

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept. Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect”, “no difference”, or “no relationship”. When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis (H A ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect”, “a difference”, or “a relationship”. When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes > or <). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

They’re both answers to the research question
They both make claims about the population
They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

Null hypothesis (H 0 ): Independent variable does not affect dependent variable .
Alternative hypothesis (H A ): Independent variable affects dependent variable .

Test-specific

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

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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9.1: Null and Alternative Hypotheses

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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

$H_0$: The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

$H_a$: The alternative hypothesis: It is a claim about the population that is contradictory to $H_0$ and what we conclude when we reject $H_0$. This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject $H_0$" if the sample information favors the alternative hypothesis or "do not reject $H_0$" or "decline to reject $H_0$" if the sample information is insufficient to reject the null hypothesis.

$H_{0}$ always has a symbol with an equal in it. $H_{a}$ never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example $\PageIndex{1}$

$H_{0}$: No more than 30% of the registered voters in Santa Clara County voted in the primary election. $p \leq 30$
$H_{a}$: More than 30% of the registered voters in Santa Clara County voted in the primary election. $p > 30$

Exercise $\PageIndex{1}$

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

$H_{0}$: The drug reduces cholesterol by 25%. $p = 0.25$
$H_{a}$: The drug does not reduce cholesterol by 25%. $p \neq 0.25$

Example $\PageIndex{2}$

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

$H_{0}: \mu = 2.0$
$H_{a}: \mu \neq 2.0$

Exercise $\PageIndex{2}$

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol $(=, \neq, \geq, <, \leq, >)$ for the null and alternative hypotheses.

$H_{0}: \mu \_ 66$
$H_{a}: \mu \_ 66$
$H_{0}: \mu = 66$
$H_{a}: \mu \neq 66$

Example $\PageIndex{3}$

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

$H_{0}: \mu \geq 5$
$H_{a}: \mu < 5$

Exercise $\PageIndex{3}$

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

$H_{0}: \mu \_ 45$
$H_{a}: \mu \_ 45$
$H_{0}: \mu \geq 45$
$H_{a}: \mu < 45$

Example $\PageIndex{4}$

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

$H_{0}: p \leq 0.066$
$H_{a}: p > 0.066$

Exercise $\PageIndex{4}$

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol ($=, \neq, \geq, <, \leq, >$) for the null and alternative hypotheses.

$H_{0}: p \_ 0.40$
$H_{a}: p \_ 0.40$
$H_{0}: p = 0.40$
$H_{a}: p > 0.40$

COLLABORATIVE EXERCISE

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

Evaluate the null hypothesis , typically denoted with $H_{0}$. The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality $(=, \leq \text{or} \geq)$
Always write the alternative hypothesis , typically denoted with $H_{a}$ or $H_{1}$, using less than, greater than, or not equals symbols, i.e., $(\neq, >, \text{or} <)$.
If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

$H_{0}$ and $H_{a}$ are contradictory.

If $\alpha \leq p$-value, then do not reject $H_{0}$.
If$\alpha > p$-value, then reject $H_{0}$.

$\alpha$ is preconceived. Its value is set before the hypothesis test starts. The $p$-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Hypothesis Testing with One Sample

Null and Alternative Hypotheses

OpenStaxCollege

[latexpage]

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H a : The alternative hypothesis: It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

H 0 : μ = 66
H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H 0 : μ ≥ 45
H a : μ < 45

H 0 : p ≤ 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

H 0 : p = 0.40
H a : p > 0.40

<!– ??? –>

Chapter Review

Formula Review

H 0 and H a are contradictory.

If α ≤ p -value, then do not reject H 0 .

If α > p -value, then reject H 0 .

α is preconceived. Its value is set before the hypothesis test starts. The p -value is calculated from the data.

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. What is the random variable? Describe in words.

The random variable is the mean Internet speed in Megabits per second.

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses.

The American family has an average of two children. What is the random variable? Describe in words.

The random variable is the mean number of children an American family has.

The mean entry level salary of an employee at a company is 💲58,000. You believe it is higher for IT professionals in the company. State the null and alternative hypotheses.

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the proportion is actually less. What is the random variable? Describe in words.

The random variable is the proportion of people picked at random in Times Square visiting the city.

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses.

In a population of fish, approximately 42% are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses.

Suppose that a recent article stated that the mean time spent in jail by a first–time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be?

H 0 : __________
H a : __________
H 0 : μ = 15
H a : μ ≠ 15

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

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

State the null hypothesis, H 0 , and the alternative hypothesis. H a , in terms of the appropriate parameter ( μ or p ).

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

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

p < 0.30
p > 0.30

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

p > 0.20
p < 0.20

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

H o : $\overline{x}$ = 4.5, H a : $\overline{x}$ > 4.5
H o : μ ≥ 4.5, H a : μ < 4.5
H o : μ = 4.75, H a : μ > 4.75
H o : μ = 4.5, H a : μ > 4.5

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm.

Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

Describe hypothesis testing in general and in practice

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H a : The alternative hypothesis : It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

After you have determined which hypothesis the sample supports, you make adecision. There are two options for a decision . They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

H a : μ ≠ 2.0

H 0 : μ = 66
H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H a : μ < 5

H 0 : μ ≥ 45
H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p ≤ 0.066

H a : p > 0.066

H 0 : p = 0.40
H a : p > 0.40

Concept Review

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

H 0 and H a are contradictory.

OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

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8.2 Null and Alternative Hypotheses

Learning objectives.

Describe hypothesis testing in general and in practice.

A hypothesis test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints and only one of these hypotheses is true. The hypothesis test determines which hypothesis is most likely true.

The null hypothesis is a claim that a population parameter equals some value. For example, [latex]H_0: \mu=5[/latex].
The alternative hypothesis is a claim that a population parameter is greater than, less than, or not equal to some value. For example, [latex]H_a: \mu>5[/latex], [latex]H_a: \mu<5[/latex], or [latex]H_a: \mu \neq 5[/latex]. The form of the alternative hypothesis depends on the wording of the hypothesis test.
An alternative notation for [latex]H_a[/latex] is [latex]H_1[/latex].

Because the null and alternative hypotheses are contradictory, we must examine evidence to decide if we have enough evidence to reject the null hypothesis or not reject the null hypothesis. The evidence is in the form of sample data. After we have determined which hypothesis the sample data supports, we make a decision. There are two options for a decision . They are “ reject [latex]H_0[/latex] ” if the sample information favors the alternative hypothesis or “ do not reject [latex]H_0[/latex] ” if the sample information is insufficient to reject the null hypothesis.

Watch this video: Simple hypothesis testing | Probability and Statistics | Khan Academy by Khan Academy [6:24]

A candidate in a local election claims that 30% of registered voters voted in a recent election. Information provided by the returning office suggests that the percentage is higher than the 30% claimed.

The parameter under study is the proportion of registered voters, so we use [latex]p[/latex] in the statements of the hypotheses. The hypotheses are

[latex]\begin{eqnarray*} \\ H_0: & & p=30\% \\ \\ H_a: & & p \gt 30\% \\ \\ \end{eqnarray*}[/latex]

The null hypothesis [latex]H_0[/latex] is the claim that the proportion of registered voters that voted equals 30%.
The alternative hypothesis [latex]H_a[/latex] is the claim that the proportion of registered voters that voted is greater than (i.e. higher) than 30%.

A medical researcher believes that a new medicine reduces cholesterol by 25%. A medical trial suggests that the percent reduction is different than claimed. State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & p=25\% \\ \\ H_a: & & p \neq 25\% \end{eqnarray*}[/latex]

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & \mu=2 \mbox{ points} \\ \\ H_a: & & \mu \neq 2 \mbox{ points} \end{eqnarray*}[/latex]

We want to test whether or not the mean height of eighth graders is 66 inches. State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & \mu=66 \mbox{ inches} \\ \\ H_a: & & \mu \neq 66 \mbox{ inches} \end{eqnarray*}[/latex]

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

[latex]\begin{eqnarray*} H_0: & & \mu=5 \mbox{ years} \\ \\ H_a: & & \mu \lt 5 \mbox{ years} \end{eqnarray*}[/latex]

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & \mu=45 \mbox{ minutes} \\ \\ H_a: & & \mu \lt 45 \mbox{ minutes} \end{eqnarray*}[/latex]

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & p=6.6\% \\ \\ H_a: & & p \gt 6.6\% \end{eqnarray*}[/latex]

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. State the null and alternative hypotheses.

[latex]\begin{eqnarray*} H_0: & & p=40\% \\ \\ H_a: & & p \gt 40\% \end{eqnarray*}[/latex]

Concept Review

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we evaluate the null hypothesis , typically denoted with [latex]H_0[/latex]. The null hypothesis is not rejected unless the hypothesis test shows otherwise. The null hypothesis always contain an equal sign ([latex]=[/latex]). Always write the alternative hypothesis , typically denoted with [latex]H_a[/latex] or [latex]H_1[/latex], using less than, greater than, or not equals symbols ([latex]\lt[/latex], [latex]\gt[/latex], [latex]\neq[/latex]). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. But we can never state that a claim is proven true or false. All we can conclude from the hypothesis test is which of the hypothesis is most likely true. Because the underlying facts about hypothesis testing is based on probability laws, we can talk only in terms of non-absolute certainties.

Attribution

“ 9.1 Null and Alternative Hypotheses “ in Introductory Statistics by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.

Hypothesis Testing: Null Hypothesis and Alternative Hypothesis

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examples of a null and alternative hypothesis

Figuring out exactly what the null hypothesis and the alternative hypotheses are is not a walk in the park. Hypothesis testing is based on the knowledge that you can acquire by going over what we have previously covered about statistics in our blog.

So, if you don’t want to have a hard time keeping up, make sure you have read all the tutorials about confidence intervals , distributions , z-tables and t-tables .

We've also made a video on null hypothesis vs alternative hypothesis - you can watch it below or just scroll down if you prefer reading.

Confidence intervals, distributions, z-tables and t-tables

Confidence intervals provide us with an estimation of where the parameters are located. You can obtain them with our confidence interval calculator and learn more about them in the related article.

However, when we are making a decision, we need a yes or no answer. The correct approach, in this case, is to use a test .

Here we will start learning about one of the fundamental tasks in statistics - hypothesis testing !

The Hypothesis Testing Process

First off, let’s talk about data-driven decision-making. It consists of the following steps:

First, we must formulate a hypothesis .
After doing that, we have to find the right test for our hypothesis .
Then, we execute the test.
Finally, we make a decision based on the result.

Steps in data driven decision making, null hypothesis

Let’s start from the beginning.

What is a Hypothesis?

Though there are many ways to define it, the most intuitive must be:

“A hypothesis is an idea that can be tested.”

This is not the formal definition, but it explains the point very well.

So, if we say that apples in New York are expensive, this is an idea or a statement. However, it is not testable, until we have something to compare it with.

Apples in New York are expensive, null hypothesis

For instance, if we define expensive as: any price higher than $1.75 dollars per pound, then it immediately becomes a hypothesis .

What Cannot Be a Hypothesis?

An example may be: would the USA do better or worse under a Clinton administration, compared to a Trump administration? Statistically speaking, this is an idea , but there is no data to test it. Therefore, it cannot be a hypothesis of a statistical test.

No data, cannot be tested = not a hypothesis

Actually, it is more likely to be a topic of another discipline.

Conversely, in statistics, we may compare different US presidencies that have already been completed. For example, the Obama administration and the Bush administration, as we have data on both.

A Two-Sided Test

Alright, let’s get out of politics and get into hypotheses . Here’s a simple topic that CAN be tested.

According to Glassdoor (the popular salary information website), the mean data scientist salary in the US is 113,000 dollars.

So, we want to test if their estimate is correct.

The Null and Alternative Hypotheses

There are two hypotheses that are made: the null hypothesis , denoted H 0 , and the alternative hypothesis , denoted H 1 or H A .

Null hypothesis and alternative hypothesis

The null hypothesis is the one to be tested and the alternative is everything else. In our example:

The null hypothesis would be: The mean data scientist salary is 113,000 dollars.

While the alternative : The mean data scientist salary is not 113,000 dollars.

Author's note: If you're interested in a data scientist career, check out our articles Data Scientist Career Path , 5 Business Basics for Data Scientists , Data Science Interview Questions , and 15 Data Science Consulting Companies Hiring Now .

An Example of a One-Sided Test

You can also form one-sided or one-tailed tests.

Say your friend, Paul, told you that he thinks data scientists earn more than 125,000 dollars per year. You doubt him, so you design a test to see who’s right.

The null hypothesis of this test would be: The mean data scientist salary is more than 125,000 dollars.

The alternative will cover everything else, thus: The mean data scientist salary is less than or equal to 125,000 dollars.

Important: The outcomes of tests refer to the population parameter rather than the sample statistic! So, the result that we get is for the population.

Important: Another crucial consideration is that, generally, the researcher is trying to reject the null hypothesis . Think about the null hypothesis as the status quo and the alternative as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging.

Let’s go over it once more. In statistics, the null hypothesis is the statement we are trying to reject. Therefore, the null hypothesis is the present state of affairs, while the alternative is our personal opinion.

The null hypothesis is the present state of affairs, while the alternative is our personal opinion

Why Hypothesis Testing Works

Right now, you may be feeling a little puzzled. This is normal because this whole concept is counter-intuitive at the beginning. However, there is an extremely easy way to continue your journey of exploring it. By diving into the linked tutorial, you will find out why hypothesis testing actually works.

Interested in learning more? You can take your skills from good to great with our statistics course!

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Next Tutorial: Hypothesis Testing: Significance Level and Rejection Region

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Course: ap®︎/college statistics > unit 10.

Idea behind hypothesis testing
Examples of null and alternative hypotheses

Writing null and alternative hypotheses

P-values and significance tests
Comparing P-values to different significance levels
Estimating a P-value from a simulation
Estimating P-values from simulations
Using P-values to make conclusions
(Choice A) H 0 : p = 0.1 H a : p ≠ 0.1 ‍ A H 0 : p = 0.1 H a : p ≠ 0.1 ‍
(Choice B) H 0 : p ≠ 0.1 H a : p = 0.1 ‍ B H 0 : p ≠ 0.1 H a : p = 0.1 ‍
(Choice C) H 0 : p = 0.1 H a : p > 0.1 ‍ C H 0 : p = 0.1 H a : p > 0.1 ‍
(Choice D) H 0 : p = 0.1 H a : p < 0.1 ‍ D H 0 : p = 0.1 H a : p < 0.1 ‍

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10.1 - setting the hypotheses: examples.

A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.

Example 10.2: Hypotheses with One Sample of One Categorical Variable Section

About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.

Research Question : Are artists more likely to be left-handed than people found in the general population?
Response Variable : Classification of the student as either right-handed or left-handed

State Null and Alternative Hypotheses

Null Hypothesis : Students in the College of Arts and Architecture are no more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Art and Architecture = 10% or p = .10).
Alternative Hypothesis : Students in the College of Arts and Architecture are more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Arts and Architecture > 10% or p > .10). This is a one-sided alternative hypothesis.

Example 10.3: Hypotheses with One Sample of One Measurement Variable Section

A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.

Research Question : Does the data suggest that the population mean dosage of this brand is different than 50 mg?
Response Variable : dosage of the active ingredient found by a chemical assay.
Null Hypothesis : On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg).
Alternative Hypothesis : On the average, the dosage sold under this brand is not 50 mg (population mean dosage ≠ 50 mg). This is a two-sided alternative hypothesis.

Example 10.4: Hypotheses with Two Samples of One Categorical Variable Section

Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.

Research Question : Does the data suggest that females are more likely than males to eat vegetarian meals on a regular basis?
Response Variable : Classification of whether or not a person eats vegetarian meals on a regular basis
Explanatory (Grouping) Variable: Sex
Null Hypothesis : There is no sex effect regarding those who eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis = population percent of males who eat vegetarian meals on a regular basis or p females = p males ).
Alternative Hypothesis : Females are more likely than males to eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis > population percent of males who eat vegetarian meals on a regular basis or p females > p males ). This is a one-sided alternative hypothesis.

Example 10.5: Hypotheses with Two Samples of One Measurement Variable Section

Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.

Research Question : Does the data suggest that, on the average, people are able to lose more weight on a low carbohydrate diet than on a low fat diet?
Response Variable : Weight loss (pounds)
Explanatory (Grouping) Variable : Type of diet
Null Hypothesis : There is no difference in the mean amount of weight loss when comparing a low carbohydrate diet with a low fat diet (population mean weight loss on a low carbohydrate diet = population mean weight loss on a low fat diet).
Alternative Hypothesis : The mean weight loss should be greater for those on a low carbohydrate diet when compared with those on a low fat diet (population mean weight loss on a low carbohydrate diet > population mean weight loss on a low fat diet). This is a one-sided alternative hypothesis.

Example 10.6: Hypotheses about the relationship between Two Categorical Variables Section

Research Question : Do the odds of having a stroke increase if you inhale second hand smoke ? A case-control study of non-smoking stroke patients and controls of the same age and occupation are asked if someone in their household smokes.
Variables : There are two different categorical variables (Stroke patient vs control and whether the subject lives in the same household as a smoker). Living with a smoker (or not) is the natural explanatory variable and having a stroke (or not) is the natural response variable in this situation.
Null Hypothesis : There is no relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is = 1).
Alternative Hypothesis : There is a relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is > 1). This is a one-tailed alternative.

This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.

Example 10.7: Hypotheses about the relationship between Two Measurement Variables Section

Research Question : A financial analyst believes there might be a positive association between the change in a stock's price and the amount of the stock purchased by non-management employees the previous day (stock trading by management being under "insider-trading" regulatory restrictions).
Variables : Daily price change information (the response variable) and previous day stock purchases by non-management employees (explanatory variable). These are two different measurement variables.
Null Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) = 0.
Alternative Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) > 0. This is a one-sided alternative hypothesis.

Example 10.8: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples Section

Calculation of a person's approximate tip for their meal

Research Question : Is there a linear relationship between the amount of the bill (\$) at a restaurant and the tip (\$) that was left. Is the strength of this association different for family restaurants than for fine dining restaurants?
Variables : There are two different measurement variables. The size of the tip would depend on the size of the bill so the amount of the bill would be the explanatory variable and the size of the tip would be the response variable.
Null Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the same at family restaurants as it is at fine dining restaurants.
Alternative Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the difference at family restaurants then it is at fine dining restaurants. This is a two-sided alternative hypothesis.

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Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.

In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.

Null Hypothesis (H 0 ) – This can be thought of as the implied hypothesis. “Null” meaning “nothing.” This hypothesis states that there is no difference between groups or no relationship between variables. The null hypothesis is a presumption of status quo or no change.
Alternative Hypothesis (H a ) – This is also known as the claim. This hypothesis should state what you expect the data to show, based on your research on the topic. This is your answer to your research question.

Null Hypothesis: H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis : H a : Male factory workers have a higher salary than female factory workers.

Null Hypothesis : H 0 : There is no relationship between height and shoe size. Alternative Hypothesis : H a : There is a positive relationship between height and shoe size.

Null Hypothesis : H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis : H a : The quality of a brick mason’s work is influenced by on-the-job experience.

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Null Hypothesis Examples

The null hypothesis (H 0 ) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment .

The null hypothesis is the most powerful type of hypothesis in the scientific method because it’s the easiest one to test with a high confidence level using statistics. If the null hypothesis is accepted, then it’s evidence any observed differences between two experiment groups are due to random chance. If the null hypothesis is rejected, then it’s strong evidence there is a true difference between test sets or that the independent variable affects the dependent variable.

The null hypothesis is a nullifiable hypothesis. A researcher seeks to reject it because this result strongly indicates observed differences are real and not just due to chance.
The null hypothesis may be accepted or rejected, but not proven. There is always a level of confidence in the outcome.

What Is the Null Hypothesis?

The null hypothesis is written as H 0 , which is read as H-zero, H-nought, or H-null. It is associated with another hypothesis, called the alternate or alternative hypothesis H A or H 1 . When the null hypothesis and alternate hypothesis are written mathematically, they cover all possible outcomes of an experiment.

An experimenter tests the null hypothesis with a statistical analysis called a significance test. The significance test determines the likelihood that the results of the test are not due to chance. Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01). But, even if the confidence in the test is high, there is always a small chance the outcome is incorrect. This means you can’t prove a null hypothesis. It’s also a good reason why it’s important to repeat experiments.

Exact and Inexact Null Hypothesis

The most common type of null hypothesis assumes no difference between two samples or groups or no measurable effect of a treatment. This is the exact hypothesis . If you’re asked to state a null hypothesis for a science class, this is the one to write. It is the easiest type of hypothesis to test and is the only one accepted for certain types of analysis. Examples include:

There is no difference between two groups H 0 : μ 1 = μ 2 (where H 0 = the null hypothesis, μ 1 = the mean of population 1, and μ 2 = the mean of population 2)

Both groups have value of 100 (or any number or quality) H 0 : μ = 100

However, sometimes a researcher may test an inexact hypothesis . This type of hypothesis specifies ranges or intervals. Examples include:

Recovery time from a treatment is the same or worse than a placebo: H 0 : μ ≥ placebo time

There is a 5% or less difference between two groups: H 0 : 95 ≤ μ ≤ 105

An inexact hypothesis offers “directionality” about a phenomenon. For example, an exact hypothesis can indicate whether or not a treatment has an effect, while an inexact hypothesis can tell whether an effect is positive of negative. However, an inexact hypothesis may be harder to test and some scientists and statisticians disagree about whether it’s a true null hypothesis .

How to State the Null Hypothesis

To state the null hypothesis, first state what you expect the experiment to show. Then, rephrase the statement in a form that assumes there is no relationship between the variables or that a treatment has no effect.

Example: A researcher tests whether a new drug speeds recovery time from a certain disease. The average recovery time without treatment is 3 weeks.

State the goal of the experiment: “I hope the average recovery time with the new drug will be less than 3 weeks.”
Rephrase the hypothesis to assume the treatment has no effect: “If the drug doesn’t shorten recovery time, then the average time will be 3 weeks or longer.” Mathematically: H 0 : μ ≥ 3

This null hypothesis (inexact hypothesis) covers both the scenario in which the drug has no effect and the one in which the drugs makes the recovery time longer. The alternate hypothesis is that average recovery time will be less than three weeks:

H A : μ < 3

Of course, the researcher could test the no-effect hypothesis (exact null hypothesis): H 0 : μ = 3

The danger of testing this hypothesis is that rejecting it only implies the drug affected recovery time (not whether it made it better or worse). This is because the alternate hypothesis is:

H A : μ ≠ 3 (which includes μ <3 and μ >3)

Even though the no-effect null hypothesis yields less information, it’s used because it’s easier to test using statistics. Basically, testing whether something is unchanged/changed is easier than trying to quantify the nature of the change.

Remember, a researcher hopes to reject the null hypothesis because this supports the alternate hypothesis. Also, be sure the null and alternate hypothesis cover all outcomes. Finally, remember a simple true/false, equal/unequal, yes/no exact hypothesis is easier to test than a more complex inexact hypothesis.

Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007). Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing. ISBN 978-90-79418-01-5 .
Cox, D. R. (2006). Principles of Statistical Inference . Cambridge University Press. ISBN 978-0-521-68567-2 .
Everitt, Brian (1998). The Cambridge Dictionary of Statistics . Cambridge, UK New York: Cambridge University Press. ISBN 978-0521593465.
Weiss, Neil A. (1999). Introductory Statistics (5th ed.). ISBN 9780201598773.

Statistics Made Easy

What is an Alternative Hypothesis in Statistics?

Often in statistics we want to test whether or not some assumption is true about a population parameter .

For example, we might assume that the mean weight of a certain population of turtle is 300 pounds.

To determine if this assumption is true, we’ll go out and collect a sample of turtles and weigh each of them. Using this sample data, we’ll conduct a hypothesis test .

The first step in a hypothesis test is to define the null and alternative hypotheses .

These two hypotheses need to be mutually exclusive, so if one is true then the other must be false.

These two hypotheses are defined as follows:

Null hypothesis (H 0 ): The sample data is consistent with the prevailing belief about the population parameter.

Alternative hypothesis (H A ): The sample data suggests that the assumption made in the null hypothesis is not true. In other words, there is some non-random cause influencing the data.

Types of Alternative Hypotheses

There are two types of alternative hypotheses:

A one-tailed hypothesis involves making a “greater than” or “less than ” statement. For example, suppose we assume the mean height of a male in the U.S. is greater than or equal to 70 inches.

The null and alternative hypotheses in this case would be:

Null hypothesis: µ ≥ 70 inches
Alternative hypothesis: µ < 70 inches

A two-tailed hypothesis involves making an “equal to” or “not equal to” statement. For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches.

Null hypothesis: µ = 70 inches
Alternative hypothesis: µ ≠ 70 inches

Note: The “equal” sign is always included in the null hypothesis, whether it is =, ≥, or ≤.

Examples of Alternative Hypotheses

The following examples illustrate how to define the null and alternative hypotheses for different research problems.

Example 1: A biologist wants to test if the mean weight of a certain population of turtle is different from the widely-accepted mean weight of 300 pounds.

The null and alternative hypothesis for this research study would be:

Null hypothesis: µ = 300 pounds
Alternative hypothesis: µ ≠ 300 pounds

If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean weight of this population of turtles is different from 300 pounds.

Example 2: An engineer wants to test whether a new battery can produce higher mean watts than the current industry standard of 50 watts.

Null hypothesis: µ ≤ 50 watts
Alternative hypothesis: µ > 50 watts

If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean watts produced by the new battery is greater than the current industry standard of 50 watts.

Example 3: A botanist wants to know if a new gardening method produces less waste than the standard gardening method that produces 20 pounds of waste.

Null hypothesis: µ ≥ 20 pounds
Alternative hypothesis: µ < 20 pounds

If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean weight produced by this new gardening method is less than 20 pounds.

When to Reject the Null Hypothesis

Whenever we conduct a hypothesis test, we use sample data to calculate a test-statistic and a corresponding p-value.

If the p-value is less than some significance level (common choices are 0.10, 0.05, and 0.01), then we reject the null hypothesis.

This means we have sufficient evidence from the sample data to say that the assumption made by the null hypothesis is not true.

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

This means our sample data did not provide us with evidence that the assumption made by the null hypothesis was not true.

Additional Resource: An Explanation of P-Values and Statistical Significance

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Educational Research Basics by Del Siegle

Null and alternative hypotheses.

Converting research questions to hypothesis is a simple task. Take the questions and make it a positive statement that says a relationship exists (correlation studies) or a difference exists between the groups (experiment study) and you have the alternative hypothesis. Write the statement such that a relationship does not exist or a difference does not exist and you have the null hypothesis. You can reverse the process if you have a hypothesis and wish to write a research question.

When you are comparing two groups, the groups are the independent variable. When you are testing whether something affects something else, the cause is the independent variable. The independent variable is the one you manipulate.

Teachers given higher pay will have more positive attitudes toward children than teachers given lower pay. The first step is to ask yourself “Are there two or more groups being compared?” The answer is “Yes.” What are the groups? Teachers who are given higher pay and teachers who are given lower pay. The independent variable is teacher pay. The dependent variable (the outcome) is attitude towards school.

You could also approach is another way. “Is something causing something else?” The answer is “Yes.” What is causing what? Teacher pay is causing attitude towards school. Therefore, teacher pay is the independent variable (cause) and attitude towards school is the dependent variable (outcome).

By tradition, we try to disprove (reject) the null hypothesis. We can never prove a null hypothesis, because it is impossible to prove something does not exist. We can disprove something does not exist by finding an example of it. Therefore, in research we try to disprove the null hypothesis. When we do find that a relationship (or difference) exists then we reject the null and accept the alternative. If we do not find that a relationship (or difference) exists, we fail to reject the null hypothesis (and go with it). We never say we accept the null hypothesis because it is never possible to prove something does not exist. That is why we say that we failed to reject the null hypothesis, rather than we accepted it.

Del Siegle, Ph.D. Neag School of Education – University of Connecticut [email protected] www.delsiegle.com

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

H a : The alternative hypothesis: It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 . This is usually what the researcher is trying to prove.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject H 0 " if the sample information favors the alternative hypothesis or "do not reject H 0 " or "decline to reject H 0 " if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

Example 9.1

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ .30 H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are: H 0 : μ = 2.0 H a : μ ≠ 2.0

H 0 : μ __ 66
H a : μ __ 66

Example 9.3

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are: H 0 : μ ≥ 5 H a : μ < 5

H 0 : μ __ 45
H a : μ __ 45

Example 9.4

H 0 : p __ 0.40
H a : p __ 0.40

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Null Hypothesis and Alternative Hypothesis

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Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different.

How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference.

The Null Hypothesis

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H 0 .

The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.

If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.

For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit . The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has a temperature of 98.6 degrees. We do not prove that this is true.

If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.

The Alternative Hypothesis

The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either H a or by H 1 .

The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis. Going back to the above example of mean human body temperature, the alternative hypothesis is “The average adult human body temperature is not 98.6 degrees Fahrenheit.”

If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.

The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook.

Null hypothesis: “ x is equal to y .” Alternative hypothesis “ x is not equal to y .”
Null hypothesis: “ x is at least y .” Alternative hypothesis “ x is less than y .”
Null hypothesis: “ x is at most y .” Alternative hypothesis “ x is greater than y .”
An Example of a Hypothesis Test
Hypothesis Test for the Difference of Two Population Proportions
What Is a P-Value?
How to Conduct a Hypothesis Test
Hypothesis Test Example
Chi-Square Goodness of Fit Test
What Level of Alpha Determines Statistical Significance?
How to Do Hypothesis Tests With the Z.TEST Function in Excel
The Difference Between Type I and Type II Errors in Hypothesis Testing
Type I and Type II Errors in Statistics
The Runs Test for Random Sequences
What 'Fail to Reject' Means in a Hypothesis Test
What Is the Difference Between Alpha and P-Values?
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Example of a Chi-Square Goodness of Fit Test
Null Hypothesis Definition and Examples

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10.2.1: Null and Alternative Hypotheses (Exercises)

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Exercise $\PageIndex{5}$

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. What is the random variable? Describe in words.

The random variable is the mean Internet speed in Megabits per second.

Exercise $\PageIndex{1}$

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses.

The American family has an average of two children. What is the random variable? Describe in words.

The random variable is the mean number of children an American family has.

Exercise 9.2.8

The mean entry level salary of an employee at a company is $58,000. You believe it is higher for IT professionals in the company. State the null and alternative hypotheses.

Exercise 9.2.9

The random variable is the proportion of people picked at random in Times Square visiting the city.

Exercise 9.2.10

Exercise 9.2.11

In a population of fish, approximately 42% are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses.

$H_{0}: p = 0.42$
$H_{a}: p < 0.42$

Exercise 9.2.12

$H_{0}$:_______
$H_{a}$:_______

Exercise 9.2.13

$H_{0}$:_________
$H_{a}$:_________
$H_{0}: \mu = 15$
$H_{a}: \mu \neq 15$

The National Institute 9.2.14 of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?

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How to Write a Hypothesis? Types and Examples

All research studies involve the use of the scientific method, which is a mathematical and experimental technique used to conduct experiments by developing and testing a hypothesis or a prediction about an outcome. Simply put, a hypothesis is a suggested solution to a problem. It includes elements that are expressed in terms of relationships with each other to explain a condition or an assumption that hasn’t been verified using facts. 1 The typical steps in a scientific method include developing such a hypothesis, testing it through various methods, and then modifying it based on the outcomes of the experiments.

A research hypothesis can be defined as a specific, testable prediction about the anticipated results of a study. 2 Hypotheses help guide the research process and supplement the aim of the study. After several rounds of testing, hypotheses can help develop scientific theories. 3 Hypotheses are often written as if-then statements.

Here are two hypothesis examples:

Dandelions growing in nitrogen-rich soils for two weeks develop larger leaves than those in nitrogen-poor soils because nitrogen stimulates vegetative growth. 4

If a company offers flexible work hours, then their employees will be happier at work. 5

What is a hypothesis?
Types of hypotheses
Characteristics of a hypothesis
Functions of a hypothesis
How to write a hypothesis
Hypothesis examples
Frequently asked questions

What is a hypothesis?

A hypothesis expresses an expected relationship between variables in a study and is developed before conducting any research. Hypotheses are not opinions but rather are expected relationships based on facts and observations. They help support scientific research and expand existing knowledge. An incorrectly formulated hypothesis can affect the entire experiment leading to errors in the results so it’s important to know how to formulate a hypothesis and develop it carefully.

A few sources of a hypothesis include observations from prior studies, current research and experiences, competitors, scientific theories, and general conditions that can influence people. Figure 1 depicts the different steps in a research design and shows where exactly in the process a hypothesis is developed. 4

There are seven different types of hypotheses—simple, complex, directional, nondirectional, associative and causal, null, and alternative.

Types of hypotheses

The seven types of hypotheses are listed below: 5 , 6,7

Simple : Predicts the relationship between a single dependent variable and a single independent variable.

Example: Exercising in the morning every day will increase your productivity.

Complex : Predicts the relationship between two or more variables.

Example: Spending three hours or more on social media daily will negatively affect children’s mental health and productivity, more than that of adults.

Directional : Specifies the expected direction to be followed and uses terms like increase, decrease, positive, negative, more, or less.

Example: The inclusion of intervention X decreases infant mortality compared to the original treatment.

Non-directional : Does not predict the exact direction, nature, or magnitude of the relationship between two variables but rather states the existence of a relationship. This hypothesis may be used when there is no underlying theory or if findings contradict prior research.

Example: Cats and dogs differ in the amount of affection they express.

Associative and causal : An associative hypothesis suggests an interdependency between variables, that is, how a change in one variable changes the other.

Example: There is a positive association between physical activity levels and overall health.

A causal hypothesis, on the other hand, expresses a cause-and-effect association between variables.

Example: Long-term alcohol use causes liver damage.

Null : Claims that the original hypothesis is false by showing that there is no relationship between the variables.

Example: Sleep duration does not have any effect on productivity.

Alternative : States the opposite of the null hypothesis, that is, a relationship exists between two variables.

Example: Sleep duration affects productivity.

Characteristics of a hypothesis

So, what makes a good hypothesis? Here are some important characteristics of a hypothesis. 8,9

Testable : You must be able to test the hypothesis using scientific methods to either accept or reject the prediction.
Falsifiable : It should be possible to collect data that reject rather than support the hypothesis.
Logical : Hypotheses shouldn’t be a random guess but rather should be based on previous theories, observations, prior research, and logical reasoning.
Positive : The hypothesis statement about the existence of an association should be positive, that is, it should not suggest that an association does not exist. Therefore, the language used and knowing how to phrase a hypothesis is very important.
Clear and accurate : The language used should be easily comprehensible and use correct terminology.
Relevant : The hypothesis should be relevant and specific to the research question.
Structure : Should include all the elements that make a good hypothesis: variables, relationship, and outcome.

Functions of a hypothesis

The following list mentions some important functions of a hypothesis: 1

Maintains the direction and progress of the research.
Expresses the important assumptions underlying the proposition in a single statement.
Establishes a suitable context for researchers to begin their investigation and for readers who are referring to the final report.
Provides an explanation for the occurrence of a specific phenomenon.
Ensures selection of appropriate and accurate facts necessary and relevant to the research subject.

To summarize, a hypothesis provides the conceptual elements that complete the known data, conceptual relationships that systematize unordered elements, and conceptual meanings and interpretations that explain the unknown phenomena. 1

How to write a hypothesis

Listed below are the main steps explaining how to write a hypothesis. 2,4,5

Make an observation and identify variables : Observe the subject in question and try to recognize a pattern or a relationship between the variables involved. This step provides essential background information to begin your research.

For example, if you notice that an office’s vending machine frequently runs out of a specific snack, you may predict that more people in the office choose that snack over another.

Identify the main research question : After identifying a subject and recognizing a pattern, the next step is to ask a question that your hypothesis will answer.

For example, after observing employees’ break times at work, you could ask “why do more employees take breaks in the morning rather than in the afternoon?”

Conduct some preliminary research to ensure originality and novelty : Your initial answer, which is your hypothesis, to the question is based on some pre-existing information about the subject. However, to ensure that your hypothesis has not been asked before or that it has been asked but rejected by other researchers you would need to gather additional information.

For example, based on your observations you might state a hypothesis that employees work more efficiently when the air conditioning in the office is set at a lower temperature. However, during your preliminary research you find that this hypothesis was proven incorrect by a prior study.

Develop a general statement : After your preliminary research has confirmed the originality of your proposed answer, draft a general statement that includes all variables, subjects, and predicted outcome. The statement could be if/then or declarative.
Finalize the hypothesis statement : Use the PICOT model, which clarifies how to word a hypothesis effectively, when finalizing the statement. This model lists the important components required to write a hypothesis.

P opulation: The specific group or individual who is the main subject of the research

I nterest: The main concern of the study/research question

C omparison: The main alternative group

O utcome: The expected results

T ime: Duration of the experiment

Once you’ve finalized your hypothesis statement you would need to conduct experiments to test whether the hypothesis is true or false.

Hypothesis examples

The following table provides examples of different types of hypotheses. 10 ,11

Key takeaways

Here’s a summary of all the key points discussed in this article about how to write a hypothesis.

A hypothesis is an assumption about an association between variables made based on limited evidence, which should be tested.
A hypothesis has four parts—the research question, independent variable, dependent variable, and the proposed relationship between the variables.
The statement should be clear, concise, testable, logical, and falsifiable.
There are seven types of hypotheses—simple, complex, directional, non-directional, associative and causal, null, and alternative.
A hypothesis provides a focus and direction for the research to progress.
A hypothesis plays an important role in the scientific method by helping to create an appropriate experimental design.

Frequently asked questions

Hypotheses and research questions have different objectives and structure. The following table lists some major differences between the two. 9

Here are a few examples to differentiate between a research question and hypothesis.

Yes, here’s a simple checklist to help you gauge the effectiveness of your hypothesis. 9 1. When writing a hypothesis statement, check if it: 2. Predicts the relationship between the stated variables and the expected outcome. 3. Uses simple and concise language and is not wordy. 4. Does not assume readers’ knowledge about the subject. 5. Has observable, falsifiable, and testable results.

As mentioned earlier in this article, a hypothesis is an assumption or prediction about an association between variables based on observations and simple evidence. These statements are usually generic. Research objectives, on the other hand, are more specific and dictated by hypotheses. The same hypothesis can be tested using different methods and the research objectives could be different in each case. For example, Louis Pasteur observed that food lasts longer at higher altitudes, reasoned that it could be because the air at higher altitudes is cleaner (with fewer or no germs), and tested the hypothesis by exposing food to air cleaned in the laboratory. 12 Thus, a hypothesis is predictive—if the reasoning is correct, X will lead to Y—and research objectives are developed to test these predictions.

Null hypothesis testing is a method to decide between two assumptions or predictions between variables (null and alternative hypotheses) in a statistical relationship in a sample. The null hypothesis, denoted as H 0 , claims that no relationship exists between variables in a population and any relationship in the sample reflects a sampling error or occurrence by chance. The alternative hypothesis, denoted as H 1 , claims that there is a relationship in the population. In every study, researchers need to decide whether the relationship in a sample occurred by chance or reflects a relationship in the population. This is done by hypothesis testing using the following steps: 13 1. Assume that the null hypothesis is true. 2. Determine how likely the sample relationship would be if the null hypothesis were true. This probability is called the p value. 3. If the sample relationship would be extremely unlikely, reject the null hypothesis and accept the alternative hypothesis. If the relationship would not be unlikely, accept the null hypothesis.

To summarize, researchers should know how to write a good hypothesis to ensure that their research progresses in the required direction. A hypothesis is a testable prediction about any behavior or relationship between variables, usually based on facts and observation, and states an expected outcome.

We hope this article has provided you with essential insight into the different types of hypotheses and their functions so that you can use them appropriately in your next research project.

References

Dalen, DVV. The function of hypotheses in research. Proquest website. Accessed April 8, 2024. https://www.proquest.com/docview/1437933010?pq-origsite=gscholar&fromopenview=true&sourcetype=Scholarly%20Journals&imgSeq=1
McLeod S. Research hypothesis in psychology: Types & examples. SimplyPsychology website. Updated December 13, 2023. Accessed April 9, 2024. https://www.simplypsychology.org/what-is-a-hypotheses.html
Scientific method. Britannica website. Updated March 14, 2024. Accessed April 9, 2024. https://www.britannica.com/science/scientific-method
The hypothesis in science writing. Accessed April 10, 2024. https://berks.psu.edu/sites/berks/files/campus/HypothesisHandout_Final.pdf
How to develop a hypothesis (with elements, types, and examples). Indeed.com website. Updated February 3, 2023. Accessed April 10, 2024. https://www.indeed.com/career-advice/career-development/how-to-write-a-hypothesis
Types of research hypotheses. Excelsior online writing lab. Accessed April 11, 2024. https://owl.excelsior.edu/research/research-hypotheses/types-of-research-hypotheses/
What is a research hypothesis: how to write it, types, and examples. Researcher.life website. Published February 8, 2023. Accessed April 11, 2024. https://researcher.life/blog/article/how-to-write-a-research-hypothesis-definition-types-examples/
Developing a hypothesis. Pressbooks website. Accessed April 12, 2024. https://opentext.wsu.edu/carriecuttler/chapter/developing-a-hypothesis/
What is and how to write a good hypothesis in research. Elsevier author services website. Accessed April 12, 2024. https://scientific-publishing.webshop.elsevier.com/manuscript-preparation/what-how-write-good-hypothesis-research/
How to write a great hypothesis. Verywellmind website. Updated March 12, 2023. Accessed April 13, 2024. https://www.verywellmind.com/what-is-a-hypothesis-2795239
15 Hypothesis examples. Helpfulprofessor.com Published September 8, 2023. Accessed March 14, 2024. https://helpfulprofessor.com/hypothesis-examples/
Editage insights. What is the interconnectivity between research objectives and hypothesis? Published February 24, 2021. Accessed April 13, 2024. https://www.editage.com/insights/what-is-the-interconnectivity-between-research-objectives-and-hypothesis
Understanding null hypothesis testing. BCCampus open publishing. Accessed April 16, 2024. https://opentextbc.ca/researchmethods/chapter/understanding-null-hypothesis-testing/#:~:text=In%20null%20hypothesis%20testing%2C%20this,said%20to%20be%20statistically%20significant

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Null & Alternative Hypotheses
The null hypothesis (H 0) answers "No, there's no effect in the population." The alternative hypothesis (H a) answers "Yes, there is an effect in the population." The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
How to Write a Null Hypothesis (5 Examples)
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. HA (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign.
Null and Alternative Hypotheses
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
9.1 Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
9.1: Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. $H_0$: The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
Examples of null and alternative hypotheses
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
Null Hypothesis: Definition, Rejecting & Examples
Alternative Hypothesis H A: The correlation in the population is not zero: ρ ≠ 0. For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis. The preceding examples are all for two-tailed hypothesis tests.
Null and Alternative Hypotheses
H a: The alternative hypothesis: It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
8.2 Null and Alternative Hypotheses
The null hypothesis is a claim that a population parameter equals some value. For example, H 0: μ = 5 H 0: μ = 5. The alternative hypothesis is denoted H a H a. It is a claim about the population that is contradictory to the null hypothesis and is what we conclude is true when we reject H 0 H 0. The alternative hypothesis is a claim that a ...
Null Hypothesis and Alternative Hypothesis
The Null and Alternative Hypotheses. There are two hypotheses that are made: the null hypothesis, denoted H 0, and the alternative hypothesis, denoted H 1 or H A. The null hypothesis is the one to be tested and the alternative is everything else. In our example: The null hypothesis would be: The mean data scientist salary is 113,000 dollars.
Writing null and alternative hypotheses
Writing null and alternative hypotheses. A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of 500 tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10 % of the entire ...
10.1
10.1 - Setting the Hypotheses: Examples. A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or ...
Null & Alternative Hypotheses
Examples: Null Hypothesis: H 0: There is no difference in the salary of factory workers based on gender. Alternative Hypothesis: H a: Male factory workers have a higher salary than female factory workers. Null Hypothesis: H 0: There is no relationship between height and shoe size. Alternative Hypothesis: H a: There is a positive relationship ...
Null Hypothesis Examples
An example of the null hypothesis is that light color has no effect on plant growth. The null hypothesis (H 0) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment.
What is an Alternative Hypothesis in Statistics?
Null hypothesis: µ ≥ 70 inches. Alternative hypothesis: µ < 70 inches. A two-tailed hypothesis involves making an "equal to" or "not equal to" statement. For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches. The null and alternative hypotheses in this case would be: Null hypothesis: µ = 70 inches.
10.2: Null and Alternative Hypotheses
The alternative hypothesis ( Ha H a) is a claim about the population that is contradictory to H0 H 0 and what we conclude when we reject H0 H 0. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample ...
9.1 Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement of no difference between the variables-they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
Null and Alternative Hypotheses
If we do not find that a relationship (or difference) exists, we fail to reject the null hypothesis (and go with it). We never say we accept the null hypothesis because it is never possible to prove something does not exist. That is why we say that we failed to reject the null hypothesis, rather than we accepted it. Del Siegle, Ph.D.
9.1 Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
Null Hypothesis and Alternative Hypothesis
For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit.The null hypothesis for an experiment to investigate this is "The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit."
10.2.1: Null and Alternative Hypotheses (Exercises)
State the null and alternative hypotheses. Answer. \ (H_ {0}: p = 0.42\) \ (H_ {a}: p < 0.42\) Exercise 9.2.12. Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century.
How to Write a Hypothesis? Types and Examples
Null: Claims that the original hypothesis is false by showing that there is no relationship between the variables. Example: Sleep duration does not have any effect on productivity. Alternative: States the opposite of the null hypothesis, that is, a relationship exists between two variables. Example: Sleep duration affects productivity.

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Null and Alternative Hypotheses | Definitions & Examples

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9.1: Null and Alternative Hypotheses

Example \(\PageIndex{1}\)

Exercise \(\PageIndex{1}\)

Example \(\PageIndex{2}\)

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Example \(\PageIndex{3}\)

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COLLABORATIVE EXERCISE

Formula Review

Null and Alternative Hypotheses

Chapter Review

Formula Review

Module 9: Hypothesis Testing With One Sample

Concept Review

Formula Review

8.2 Null and Alternative Hypotheses

Concept Review

Attribution

Hypothesis Testing: Null Hypothesis and Alternative Hypothesis

The Hypothesis Testing Process

What is a Hypothesis?

What Cannot Be a Hypothesis?

A Two-Sided Test

The Null and Alternative Hypotheses

An Example of a One-Sided Test

Why Hypothesis Testing Works

AP®︎/College Statistics

Writing null and alternative hypotheses

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Example 10.2: Hypotheses with One Sample of One Categorical Variable Section

State Null and Alternative Hypotheses

Example 10.3: Hypotheses with One Sample of One Measurement Variable Section

Example 10.4: Hypotheses with Two Samples of One Categorical Variable Section

Example 10.5: Hypotheses with Two Samples of One Measurement Variable Section

Example 10.6: Hypotheses about the relationship between Two Categorical Variables Section

Example 10.7: Hypotheses about the relationship between Two Measurement Variables Section

Example 10.8: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples Section

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Educational Research Basics by Del Siegle

9.1 Null and Alternative Hypotheses

Example 9.1

Example 9.2

Example 9.3

Example 9.4

Collaborative Exercise

Null Hypothesis and Alternative Hypothesis

The Null Hypothesis

The Alternative Hypothesis

10.2.1: Null and Alternative Hypotheses (Exercises)

How to Write a Hypothesis? Types and Examples

Table of Contents

What is a hypothesis?

Types of hypotheses

Characteristics of a hypothesis

Functions of a hypothesis