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• Null and Alternative Hypotheses | Definitions & Examples

Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.

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 or H 1 ) : There’s an effect in the population.

Table of contents

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

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.”
• 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. It’s critical for your research to write strong hypotheses .

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.

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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 ≤).

You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.

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.

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 template sentences

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.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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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• Knowledge Base
• 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 .

Table of contents

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

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.

H a —, the alternative hypothesis: 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.

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 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 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent 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 percent. 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 the following: H 0 : μ = 2.0 H a : 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

Example 9.3

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

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 : μ __ 45
• H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent 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

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.

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Alternative hypothesis

by Marco Taboga , PhD

In a statistical test, observed data is used to decide whether or not to reject a restriction on the data-generating probability distribution.

The assumption that the restriction is true is called null hypothesis , while the statement that the restriction is not true is called alternative hypothesis.

A correct specification of the alternative hypothesis is essential to decide between one-tailed and two-tailed tests.

Table of contents

Mathematical setting

Choice between one-tailed and two-tailed tests, the critical region, the interpretation of the rejection, the interpretation must be coherent with the alternative hypothesis.

• Power function

Accepting the alternative

More details, keep reading the glossary.

In order to fully understand the concept of alternative hypothesis, we need to remember the essential elements of a statistical inference problem:

we observe a sample drawn from an unknown probability distribution;

in principle, any valid probability distribution could have generated the sample;

however, we usually place some a priori restrictions on the set of possible data-generating distributions;

A couple of simple examples follow.

When we conduct a statistical test, we formulate a null hypothesis as a restriction on the statistical model.

The alternative hypothesis is

The alternative hypothesis is used to decide whether a test should be one-tailed or two-tailed.

The null hypothesis is rejected if the test statistic falls within a critical region that has been chosen by the statistician.

The critical region is a set of values that may comprise:

only the left tail of the distribution or only the right tail (one-tailed test);

both the left and the right tail (two-tailed test).

The choice of the critical region depends on the alternative hypothesis. Let us see why.

The interpretation is different depending on the tail of the distribution in which the test statistic falls.

The choice between a one-tailed or a two-tailed test needs to be done in such a way that the interpretation of a rejection is always coherent with the alternative hypothesis.

When we deal with the power function of a test, the term "alternative hypothesis" has a special meaning.

We conclude with a caveat about the interpretation of the outcome of a test of hypothesis.

The interpretation of a rejection of the null is controversial.

According to some statisticians, rejecting the null is equivalent to accepting the alternative.

However, others deem that rejecting the null does not necessarily imply accepting the alternative. In fact, it is possible to think of situations in which both hypotheses can be rejected. Let us see why.

According to the conceptual framework illustrated by the images above, there are three possibilities:

the null is true;

the alternative is true;

neither the null nor the alternative is true because the true data-generating distribution has been excluded from the statistical model (we say that the model is mis-specified).

If we are in case 3, accepting the alternative after a rejection of the null is an incorrect decision. Moreover, a second test in which the alternative becomes the new null may lead us to another rejection.

You can find more details about the alternative hypothesis in the lecture on Hypothesis testing .

Previous entry: Almost sure

Next entry: Binomial coefficient

How to cite

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Statistics By Jim

Making statistics intuitive

Alternative hypothesis

By Jim Frost

The alternative hypothesis is one of two mutually exclusive hypotheses in a hypothesis test. The alternative hypothesis states that a population parameter does not equal a specified value. Typically, this value is the null hypothesis value associated with no effect , such as zero. If your sample contains sufficient evidence, you can reject the null hypothesis and favor the alternative hypothesis. The alternative hypothesis is often denoted as H 1 or H A .

If you are performing a two-tailed hypothesis test, the alternative hypothesis states that the population parameter does not equal the null hypothesis value. For example, when the alternative hypothesis is H A : μ ≠ 0, the test can detect differences both greater than and less than the null value.

A one-tailed alternative hypothesis can test for a difference only in one direction. For example, H A : μ > 0 can only test for differences that are greater than zero.

• How Hypothesis Tests Work: Significance Levels (Alpha) and P values
• How to Identify the Distribution of Your Data
• When Can I Use One-Tailed Hypothesis Tests?
• Examples of Hypothesis Tests: Busting Myths about the Battle of the Sexes
• Failing to Reject the Null Hypothesis

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 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 .

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 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 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

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

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

• 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

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 : μ __ 45 H a : μ __ 45

• 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

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

• 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.

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Alternative Hypothesis: Definition, Types and Examples

In statistical hypothesis testing, the alternative hypothesis is an important proposition in the hypothesis test. The goal of the hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of the alternative hypothesis instead of the default assumption made by the null hypothesis.

Alternative Hypotheses

Both hypotheses include statements with the same purpose of providing the researcher with a basic guideline. The researcher uses the statement from each hypothesis to guide their research. In statistics, alternative hypothesis is often denoted as H a or H 1 .

Table of Content

What is a Hypothesis?

Alternative hypothesis, types of alternative hypothesis, difference between null and alternative hypothesis, formulating an alternative hypothesis, example of alternative hypothesis, application of alternative hypothesis.

“A hypothesis is a statement of a relationship between two or more variables.” It is a working statement or theory that is based on insufficient evidence.

While experimenting, researchers often make a claim, that they can test. These claims are often based on the relationship between two or more variables. “What causes what?” and “Up to what extent?” are a few of the questions that a hypothesis focuses on answering. The hypothesis can be true or false, based on complete evidence.

While there are different hypotheses, we discuss only null and alternate hypotheses. The null hypothesis, denoted H o , is the default position where variables do not have a relation with each other. That means the null hypothesis is assumed true until evidence indicates otherwise. The alternative hypothesis, denoted H 1 , on the other hand, opposes the null hypothesis. It assumes a relation between the variables and serves as evidence to reject the null hypothesis.

Example of Hypothesis:

Mean age of all college students is 20.4 years. (simple hypothesis).

An Alternative Hypothesis is a claim or a complement to the null hypothesis. If the null hypothesis predicts a statement to be true, the Alternative Hypothesis predicts it to be false. Let’s say the null hypothesis states there is no difference between height and shoe size then the alternative hypothesis will oppose the claim by stating that there is a relation.

We see that the null hypothesis assumes no relationship between the variables whereas an alternative hypothesis proposes a significant relation between variables. An alternative theory is the one tested by the researcher and if the researcher gathers enough data to support it, then the alternative hypothesis replaces 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.

There are a few types of alternative hypothesis that we will see:

1. One-tailed test H 1 : A one-tailed alternative hypothesis focuses on only one region of rejection of the sampling distribution. The region of rejection can be upper or lower.

• Upper-tailed test H 1 : Population characteristic > Hypothesized value
• Lower-tailed test H 1 : Population characteristic < Hypothesized value

2. Two-tailed test H 1 : A two-tailed alternative hypothesis is concerned with both regions of rejection of the sampling distribution.

3. Non-directional test H 1 : A non-directional alternative hypothesis is not concerned with either region of rejection; rather, it is only concerned that null hypothesis is not true.

4. Point test H 1 : Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference and are the basis of the Neyman–Pearson lemma.

the differences between Null Hypothesis and Alternative Hypothesis is explained in the table below:

Formulating an alternative hypothesis means identifying the relationships, effects or condition being studied. Based on the data we conclude that there is a different inference from the null-hypothesis being considered.

• Understand the null hypothesis.
• Consider the alternate hypothesis
• Choose the type of alternate hypothesis (one-tailed or two-tailed)

Alternative hypothesis must be true when the null hypothesis is false. When trying to identify the information need for alternate hypothesis statement, look for the following phrases:

• “Is it reasonable to conclude…”
• “Is there enough evidence to substantiate…”
• “Does the evidence suggest…”
• “Has there been a significant…”

When alternative hypotheses in mathematical terms, they always include an inequality ( usually ≠, but sometimes < or >) . When writing the alternate hypothesis, make sure it never includes an “=” symbol.

To help you write your hypotheses, you can use the template sentences below.

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.

Various examples of Alternative Hypothesis includes:

Two-Tailed Example

• Research Question : Do home games affect a team’s performance?
• Null-Hypothesis: Home games do not affect a team’s performance.
• Alternative Hypothesis: Home games have an effect on team’s performance.
• Research Question: Does sleeping less lead to depression?
• Null-Hypothesis: Sleeping less does not have an effect on depression.
• Alternative Hypothesis : Sleeping less has an effect on depression.

One-Tailed Example

• Research Question: Are candidates with experience likely to get a job?
• Null-Hypothesis: Experience does not matter in getting a job.
• Alternative Hypothesis: Candidates with work experience are more likely to receive an interview.
• Alternative Hypothesis : Teams with home advantage are more likely to win a match.

Some applications of Alternative Hypothesis includes:

• Rejecting Null-Hypothesis : A researcher performs additional research to find flaws in the null hypothesis. Following the research, which uses the alternative hypothesis as a guide, they may decide whether they have enough evidence to reject the null hypothesis.
• Guideline for Research : An alternative and null hypothesis include statements with the same purpose of providing the researcher with a basic guideline. The researcher uses the statement from each hypothesis to guide their research.
• New Theories : Alternative hypotheses can provide the opportunity to discover new theories that a researcher can use to disprove an existing theory that may not have been backed up by evidence.

We defined the relationship that exist between null-hypothesis and alternative hypothesis. While the null hypothesis is always a default assumption about our test data, the alternative hypothesis puts in all the effort to make sure the null hypothesis is disproved.

Null-hypothesis always explores new relationships between the independent variables to find potential outcomes from our test data. We should note that for every null hypothesis, one or more alternate hypotheses can be developed.

Also Check:

Mathematics Maths Formulas Branches of Mathematics

FAQs on Alternative Hypothesis

What is hypothesis.

A hypothesis is a statement of a relationship between two or more variables.” It is a working statement or theory that is based on insufficient evidence.

What is an Alternative Hypothesis?

Alternative hypothesis, denoted by H 1 , opposes the null-hypothesis. It assumes a relation between the variables and serves as an evidence to reject the null-hypothesis.

What is the Difference between Null-Hypothesis and Alternative Hypothesis?

Null hypothesis is the default claim that assumes no relationship between variables while alternative hypothesis is the opposite claim which considers statistical significance between the variables.

What is Alternative and Experimental Hypothesis?

Null hypothesis (H 0 ) states there is no effect or difference, while the alternative hypothesis (H 1 or H a ) asserts the presence of an effect, difference, or relationship between variables. In hypothesis testing, we seek evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to do so.

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Alternative Hypothesis

Alternative hypothesis defines there is a statistically important relationship between two variables. Whereas null hypothesis states there is no statistical relationship between the two variables. In statistics, we usually come across various kinds of hypotheses. A statistical hypothesis is supposed to be a working statement which is assumed to be logical with given data. It should be noticed that a hypothesis is neither considered true nor false.

The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H a or H 1 . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption. In this hypothesis, the difference between two or more variables is predicted by the researchers, such that the pattern of data observed in the test is not due to chance.

To check the water quality of a river for one year, the researchers are doing the observation. As per the null hypothesis, there is no change in water quality in the first half of the year as compared to the second half. But in the alternative hypothesis, the quality of water is poor in the second half when observed.

Difference Between Null and Alternative Hypothesis

Basically, there are three types of the alternative hypothesis, they are;

Left-Tailed : Here, it is expected that the sample proportion (π) is less than a specified value which is denoted by π 0 , such that;

H 1 : π < π 0

Right-Tailed: It represents that the sample proportion (π) is greater than some value, denoted by π 0 .

H 1 : π > π 0

Two-Tailed: According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π 0 .

H 1 : π ≠ π 0

Note: The null hypothesis for all the three alternative hypotheses, would be H 1 : π = π 0 .

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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  

• 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.

• Alternative vs Null Hypothesis: Pros, Cons, Uses & Examples

All research starts with a problem that needs to be solved. From this problem, hypotheses are developed to provide the researcher with a clear statement of the problem.

To understand alternative hypotheses also known as alternate hypotheses, you must first understand what the hypothesis is .

When you hear the word hypothesis it means the accurate explanations in relation to a set of facts that can be analyzed when studied, using some specific method of research.

There are primarily two types of hypothesis which are null hypothesis and alternative hypothesis.

When you think about the word “null” what should come to mind is something that can not change, what you expect is what you get, unlike alternate hypotheses which can change.

Now, the research problems or questions which could be in the form of null hypothesis or alternative hypothesis are expressed as the relationship that exists between two or more variables. The process for this states that the questions should be what expresses the relationship between two variables that can be measured.

Both null hypotheses and alternative hypotheses are used by statisticians and researchers to conduct research in various industries or fields such as mathematics, psychology, science, medicine, and technology.

We are going to discuss alternative hypotheses and null hypotheses in this post and how they work in research.

What is an Alternative Hypothesis?

Alternative hypothesis simply put is another viable option to the null hypothesis. It means looking for a substantial change or option that can allow you to reject the null hypothesis.

It is an opposing theory to a null hypothesis.

If you develop a null hypothesis, you make an informed guess on whether a thing is true or whether there is a relationship between that thing and another variable. An alternate hypothesis will always take an opposite stand against a null hypothesis. So if according to a null hypothesis something is correct to an alternate hypothesis that same thing will be incorrect.

For example, let’s assume that you develop a null hypothesis that states “I”m going to be $500 richer” the alternate hypothesis will be “I’m going to get $500 or be richer”

When you are trying to disprove a null hypothesis, that is when you test an alternate hypothesis. If there is enough data to back up the alternative hypothesis then you can dispose of the null hypothesis. 

Get Answers: What is Empirical Research Study? [Examples & Method]

What is a Null Hypothesis?

The null hypothesis is best explained as the statement showing that no relationship exists between two variables that are being considered or that two groups are not related. As we have earlier established, a hypothesis is an assumed statement that has not been proven with sufficient data that could serve as a piece of evidence. 

The null hypothesis is now the statement that a researcher or an investigator wants to disprove. The null hypothesis is capable of being tested, being verifiable, and also capable of being rejected.

For example, if you want to conduct a study that will compare the relationship between project A and project B if the study is based on the assumption that both projects are of equal standard, the assumption is referred to as the null hypothesis.

This is because the null hypothesis should be specific at all times.

Learn: Hypothesis Testing in Research: Definition, Procedure, Uses, Limitations + Examples

Advantages of the Alternative Hypothesis 

• Alternative hypothesis gives a researcher specific clarifications on the research questions or problems .
• It provides a study with the direction that can be used to collect data and obtain results of interest by the researcher.
• An alternative hypothesis is always selected before commencing the studies which gives the researcher the opportunity to prove that the restatement is backed up by evidence and not just from the researcher’s ideas or values.
• Another good thing about alternative hypotheses is that it provides the opportunity to discover new theories that a researcher can use to disprove an existing theory that may not have been backed up by evidence .
• An alternate hypothesis is also useful to prove that there is a relationship between two selected variables and the outcomes of the conducted study are relevant.

Principles of the Alternative Hypothesis

• Alternative hypotheses will be accepted if the amount of data that is gone is insignificant within the significance level. This means that the null hypothesis will be rejected.
• Another principle of the alternative hypothesis is that the data gathered from random samples go through a statistical tool that analyzes the effect of the amount of data leaving the null hypothesis.

For the curious: Sampling Bias: Definition, Types + [Examples]

Purpose of the Null Hypothesis 

Here are the purposes of the null hypothesis in an experiment or study:

• The primary purpose of a null hypothesis is to disprove an assumption.
• Null hypotheses can help to further progress a theory in some scientific cases.
• You can also use a null hypothesis to ascertain how consistent the outcomes of multiple studies are.

Principle of the Null Hypothesis 

Now, these are the principles of the null hypothesis:

1. The primary principle of the null hypothesis is to prove that the assumed statement is true. This is done by collecting data and analyzing in the study , what chance the collected data has in the random sample.

2. If the collected data does not meet the expectation of the null hypothesis, it is determined that the data lacks sufficient evidence to back up the null hypothesis therefore the null hypothesis statement is rejected.

Just as in the case of the alternative hypothesis the collected data in a null hypothesis is analyzed using some statistical tools that are made to measure the extent to which data left the null hypothesis.

The process will determine whether the data that left the null hypothesis is larger than a set value. If the data collected from the random sample is enough to serve as evidence to prove the null hypothesis then the null hypothesis will be accepted as true. And also defined that it has no relationship with other variables .

Learn About: Research Reports: Definition, Types + [Writing Guide]

Types of Alternative Hypothesis (Advantages of Each and When to Use)

There are four types of alternative hypotheses, and we will briefly discuss them below.

• One-tailed directional: For one of the sampling distributions one tail, this type of alternative hypothesis focuses on the rejected part only.
• Two-tailed directional: In an alternative hypothesis, a two-tailed directional focus on the two parts or directions that were rejected in the sampling distribution.
• Point: Point is another alternate hypothesis. It occurs in hypothesis testing when the sample population in the alternate hypothesis has been completely defined in a distribution. If there are no known parameters, the hypothesis will serve no interest. They are, however, important to the foundation of the statistical inferences.
• Non-directional: In an alternate hypothesis, a non-directional does not focus on the two directions of rejection. The only focus of the nondirectional alternative hypothesis is to prove that the null hypothesis is incorrect.

Read: Type I vs Type II Errors: Definition, Examples & Prevention

Difference between Null Hypothesis and Alternative Hypothesis 

We are going to look at the differences between the alternate hypothesis and the null hypothesis based on these six factors which are:

• Mathematical expression
• Observation
• Acceptance criteria
• The difference in Mathematical expression

Null hypothesis is followed by an ‘equals to’ (=) sign. While the Alternative hypothesis is followed by these three signs; 

• The difference in how they are observed

In the null hypothesis, it is believed that the results that are observed are as a result of chance. While In the alternative hypothesis, it is believed that the observed results are the outcome of some real causes.

• Differences in results

The result of the null hypothesis always shows that there have been no changes in statements or opinions. While the result of the alternative hypothesis shows that there have been significant changes in statements and opinions.

• Differences in Acceptance criteria

If the p-value in a null hypothesis is greater than the significance level, then the null hypothesis is accepted.

If the p-value in an alternate hypothesis is smaller than the significance level, then the alternative hypothesis is accepted.

• Differences in importance

The null hypothesis accepts true existing theories and also if there has been consistency in multiple experiments of similar hypotheses.

The alternative hypothesis establishes whether a relationship exists between two variables, and the result will then lead to new improved theories.

Read: T-testing: Definition, Formula & Interpretations

Examples of an Alternative Hypothesis and Null Hypothesis

Here are some examples of the alternative hypothesis:.

A researcher assumes that a bridge’s bearing capacity is over 10 tons, the researcher will then develop an hypothesis to support this study. The hypothesis will be:

For the null hypothesis H0: µ= 10 tons

For the alternate hypothesis Ha: µ>10 tons

In another study being conducted, the researcher wants to find out whether there is a noticeable difference or change in a patient’s heart arrest medicine and the patient’s heart condition.

For the alternate hypothesis: The hypothesis is that there might indeed be a relationship between the new medicine and the frequency or chances of heart arrest in a patient.

Here are the examples of the null hypothesis

The hypothesis from example 2 in the alternate hypothesis implies that the use of one specific medicine can reduce the frequency and chances of heart arrest.

For the null hypothesis: The hypothesis will be that the use of that particular medicine cannot reduce the chance and frequency of heart arrest in a patient.

An alternate hypothesis states that the random exam scores are collected from both men and women. But are the scores of the two groups (men and women) the same or are they different?

For the null hypothesis: The hypothesis will state that the calculated mean of the men’s exam score is equal to the exam score of the women.

This is represented as

H0= The null hypothesis

µ1= The calculated mean score of men

µ2= The calculated mean score of women

Read: What is Empirical Research Study? [Examples & Method]

• Can you reject an alternative hypothesis?

It is quite inappropriate to say or report that an alternate hypothesis was rejected. It is much better to use the phrase “the alternate hypothesis was rather not supported”.

The reason behind this use of words is that only the null hypothesis is designed to be rejected in a study. The alternative hypothesis is designed to prove the null hypothesis incorrect, to introduce new facts that can disprove the null hypothesis but it is not designed to be rejected.

It can either be accepted or not supported.

• How do you identify alternative hypotheses?

A researcher can use this formula to identify the alternate hypothesis in a study or experiment.

H0 and Ha are in contrast.

Therefore, if Ho has:

Equal to (=)

Greater than or equal to (≥)

Less than or equal to (≤)

And then Ha has:

Not equal (≠) 

Greater than (>) or less than (

Less than ( )

If in a study, α ≤ p-value, then the researcher should not reject H0.

If in a study, α > p-value, then the researcher should reject H0.

α is preconceived. The value of α is determined even before the hypothesis test is conducted. While the p-value is derived from the calculation in the data.

• Which is better in formulating hypotheses of your study alternative or null?

The study a researcher wants to conduct will determine what hypothesis should be developed. However, the researcher should keep in mind what the purpose of the null and alternative two hypotheses are while developing the study hypothesis. So while the null hypothesis will accept existing theories that it found to be true or correct, and measure the consistency of multiple experiments, alternative hypotheses will find the relationship that exists (if any) between two phenomena and may lead to the development of a new and improved theory.

In this article, it has been clearly defined the relationship that exists between the null hypothesis and the alternative hypothesis. While the null hypothesis is always an assumption that needs to be proven with evidence for it to be accepted, the alternative hypothesis puts in all the effort to make sure the null hypothesis is disproved. 

Researchers should note that for every null hypothesis, one or more alternate hypotheses can be developed.

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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 .”
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• The Difference Between Type I and Type II Errors in Hypothesis Testing
• What Level of Alpha Determines Statistical Significance?
• What Is the Difference Between Alpha and P-Values?
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• Example of a Permutation Test
• Degrees of Freedom for Independence of Variables in Two-Way Table
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What is an Alternative Hypothesis? Definition, Types, and Examples

The alternative hypothesis is a way to propose a contrasting view on a proposed theory by a researcher. It tries to prove the original statement provided by the null statement false.

What is an Alternative Hypothesis?

An alternative hypothesis is a contradictory theory to that taken by a Null Hypothesis about a specified research parameter.

The null hypothesis proposes that there is no relation between the independent and dependent variables in a population parameter. If the null hypothesis is true, then these variables do not change mutually.

Understanding Alternative Hypothesis

Similarly, hypothesis testing directly compares the observed data in a defined population data set with the Null hypothesis results.

Types of Alternative Hypothesis

There are two main types of alternative hypotheses.

Two-Tailed or Non-Directional Hypothesis

Examples of Alternative Hypothesis

Suppose a high school proposes that providing a laptop to all students during classes will improve their grades among other students in the school.

At the same time, the school can propose an alternative hypothesis stating:

An investment firm wants to set up an index fund following the S&P500 index. The null hypothesis states an index fund generates a 10% rate of return when followed the same way as S&P500.

Null Hypothesis Vs. Alternative Hypothesis – Key Differences

An alternative hypothesis assumes the null statement is wrong. It means it discredits the original statements or tries to prove that statement false.

Hypothesis Tests

Result Interpretations (implication)

Similarly, the alternative hypothesis can be right or wrong. Further research can propose another point of view and another alternative theory.

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