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 :

equal (=) not equal (≠) greater than (>) less than (<)
greater than or equal to (≥) less than (<)
less than or equal to (≤) more than (>)

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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  • 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.

( )
Does tooth flossing affect the number of cavities? Tooth flossing has on the number of cavities. test:

The mean number of cavities per person does not differ between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ = µ .

Does the amount of text highlighted in the textbook affect exam scores? The amount of text highlighted in the textbook has on exam scores. :

There is no relationship between the amount of text highlighted and exam scores in the population; β = 0.

Does daily meditation decrease the incidence of depression? Daily meditation the incidence of depression.* test:

The proportion of people with depression in the daily-meditation group ( ) is greater than or equal to the no-meditation group ( ) in the population; ≥ .

*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.

Does tooth flossing affect the number of cavities? Tooth flossing has an on the number of cavities. test:

The mean number of cavities per person differs between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ ≠ µ .

Does the amount of text highlighted in a textbook affect exam scores? The amount of text highlighted in the textbook has an on exam scores. :

There is a relationship between the amount of text highlighted and exam scores in the population; β ≠ 0.

Does daily meditation decrease the incidence of depression? Daily meditation the incidence of depression. test:

The proportion of people with depression in the daily-meditation group ( ) is less than the no-meditation group ( ) in the population; < .

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.

A claim that there is in the population. A claim that there is in the population.

Equality symbol (=, ≥, or ≤) Inequality symbol (≠, <, or >)
Rejected Supported
Failed to reject Not supported

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.

( )
test 

with two groups

The mean dependent variable does not differ between group 1 (µ ) and group 2 (µ ) in the population; µ = µ . The mean dependent variable differs between group 1 (µ ) and group 2 (µ ) in the population; µ ≠ µ .
with three groups The mean dependent variable does not differ between group 1 (µ ), group 2 (µ ), and group 3 (µ ) in the population; µ = µ = µ . The mean dependent variable of group 1 (µ ), group 2 (µ ), and group 3 (µ ) are not all equal in the population.
There is no correlation between independent variable and dependent variable in the population; ρ = 0. There is a correlation between independent variable and dependent variable in the population; ρ ≠ 0.
There is no relationship between independent variable and dependent variable in the population; β = 0. There is a relationship between independent variable and dependent variable in the population; β ≠ 0.
Two-proportions test The dependent variable expressed as a proportion does not differ between group 1 ( ) and group 2 ( ) in the population; = . The dependent variable expressed as a proportion differs between group 1 ( ) and group 2 ( ) in the population; ≠ .

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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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 :

equal (=) not equal (≠)
greater than (>) less than (<)
greater than or equal to (≥) less than (<)
less than or equal to (≤) more than (>)

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.

  • 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

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.

[eq1]

The alternative hypothesis is

[eq2]

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.

[eq7]

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.

[eq10]

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.

There are three cases, including one case in which it is incorrect to accept the alternative hypothesis after a rejection of the null.

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

Please cite as:

Taboga, Marco (2021). "Alternative hypothesis", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/alternative-hypothesis.

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Methodology

  • How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

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

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

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

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

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

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

  • An independent variable is something the researcher changes or controls.
  • A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

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

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Step 1. ask a question.

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

Step 2. Do some preliminary research

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

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

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

4. Refine your hypothesis

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

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

5. Phrase your hypothesis in three ways

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

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

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

6. Write a null hypothesis

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

  • H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
  • H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.
Research question Hypothesis Null hypothesis
What are the health benefits of eating an apple a day? Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits.
Which airlines have the most delays? Low-cost airlines are more likely to have delays than premium airlines. Low-cost and premium airlines are equally likely to have delays.
Can flexible work arrangements improve job satisfaction? Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. There is no relationship between working hour flexibility and job satisfaction.
How effective is high school sex education at reducing teen pregnancies? Teenagers who received sex education lessons throughout high school will have lower rates of unplanned pregnancy teenagers who did not receive any sex education. High school sex education has no effect on teen pregnancy rates.
What effect does daily use of social media have on the attention span of under-16s? There is a negative between time spent on social media and attention span in under-16s. There is no relationship between social media use and attention span in under-16s.

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

  • Sampling methods
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
  • Likert scales
  • Reproducibility

 Statistics

  • Null hypothesis
  • Statistical power
  • Probability distribution
  • Effect size
  • Poisson distribution

Research bias

  • Optimism bias
  • Cognitive bias
  • Implicit bias
  • Hawthorne effect
  • Anchoring bias
  • Explicit bias

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

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.

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.

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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  

 two Diphenhydramine pills

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  

vegetarian airline meal

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  

low carb meal

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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Alternative Hypothesis

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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

It denotes there is no relationship between two measured phenomena.

It’s a hypothesis that a random cause may influence the observed data or sample.

It is represented by H

It is represented by H or H

Example: Rohan will win at least Rs.100000 in lucky draw.

Example: Rohan will win less than Rs.100000 in lucky draw.

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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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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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.

Null-Hypothesis-and-Alternative-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:

Null Hypothesis(H )

Alternative Hypothesis(H )

Definition

A default statement that states no relationship between variables.

A claim that assumes a relationship between variables.

Denoted by

H

H or H

In Research

States a presumption made before-hand

States the potential outcome a researcher may expect

Symbols Used

Equality Symbol (=, ≥, or ≤)

Inequality Symbol (≠, <, or >)

Example

Experience matters in a tech-job

Experience does not matter in a tech-job

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.

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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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examples of alternative hypothesis statements

Diving deep into the realm of scientific research, the alternative hypothesis plays a pivotal role in steering investigations. It stands contrary to the null hypothesis , providing a different perspective or direction. This essential component often sets the foundation for groundbreaking discoveries. If you’re keen on understanding this concept further, our collection of alternative hypothesis statement examples, combined with a thorough writing guide and insightful tips, will serve as your comprehensive roadmap.

What is an Alternative hypothesis?

An alternative hypothesis is a statement used in statistical testing that indicates the presence of an effect, relationship, or difference. It stands in direct contrast to the null hypothesis, which posits that there is no effect or relationship. The alternative causual hypothesis provides a specific direction to the research and can be directional (e.g., one value is greater than another) or non-directional (e.g., two values are not equal).

What is an example of an Alternative hypothesis statement?

If a researcher is studying the effect of a new teaching method on student performance, the null hypothesis might be: “The new teaching method has no effect on student performance.” An example of an alternative hypothesis could be:

Directional: “Students exposed to the new teaching method will perform better than those who were not.” Non-directional: “Student performance will be different for those exposed to the new teaching method compared to those who were not.”

100 Alternative Hypothesis Statement Examples

Alternative Hypothesis Statement Examples

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The alternative hypothesis symbolizes a statement of what a statistical hypothesis test is set to establish. Often contrasted with a null hypothesis, it indicates the expected direction of the tested relation. Dive into these varied thesis statement examples showcasing the core essence of alternative hypotheses.

  • Smoking and Cancer : Smoking is positively related to lung cancer incidence.
  • Diet and Weight Loss : The Atkins diet results in more weight loss than a conventional diet.
  • Medication Efficiency : Drug A is more effective than Drug B in treating migraines.
  • Exercise Duration : Engaging in physical activity for more than 30 minutes daily reduces depression symptoms.
  • Class Size and Learning : Smaller class sizes lead to higher student test scores.
  • Sugar Intake : Consuming more than 50 grams of sugar daily increases the risk of diabetes.
  • Vitamin C and Cold : Vitamin C intake reduces the duration of the common cold.
  • Sleep Duration : Sleeping less than 6 hours results in decreased cognitive function.
  • Training Methods : Method X training increases employee productivity more than Method Y.
  • Pollution Levels : Higher levels of industrial activity correlate with increased air pollution.
  • Stress and Disease : Chronic stress has a positive relationship with heart diseases.
  • Alcohol and Reaction Time : Alcohol consumption slows down reaction time.
  • Meditation and Blood Pressure : Regular meditation lowers blood pressure.
  • Organic Food : Consuming organic food leads to better gut health.
  • Advertising : Increased advertising results in higher sales figures.
  • Salary and Job Satisfaction : A higher salary correlates with job satisfaction.
  • Age and Memory : As age increases, short-term memory retention decreases.
  • Temperature and Aggression : Higher temperatures are associated with increased aggressive behavior.
  • Social Media : Spending more than 2 hours on social media daily increases feelings of loneliness.
  • Music and Concentration : Listening to classical music improves concentration during studies. …
  • Recycling Habits : Communities with mandatory recycling policies have higher recycling rates.
  • Urban Areas : Living in urban areas increases the likelihood of asthma.
  • Pets and Loneliness : Owning a pet decreases feelings of loneliness.
  • Reading Habits : Reading more than 3 books a month correlates with increased empathy.
  • Green Spaces : Having access to green spaces reduces stress levels.
  • Vaccination : Vaccination reduces the incidence of specific diseases.
  • Chocolate and Mood : Consuming chocolate elevates mood.
  • Remote Work : Working remotely improves overall work satisfaction.
  • Financial Literacy : Financial literacy education reduces personal debt.
  • Mindfulness and Anxiety : Practicing mindfulness decreases symptoms of anxiety. …
  • Dietary Fiber : Higher dietary fiber intake is associated with lower risks of bowel cancer.
  • Travel and Creativity : People who travel frequently are more creative.
  • Education Level and Income : Individuals with higher education levels earn more income.
  • Technology Adoption : People who receive technology training adapt to new devices faster.
  • Parental Involvement and Academic Performance : Increased parental involvement enhances students’ academic performance.
  • Exercise Frequency and Heart Health : Exercising at least five times a week improves heart health.
  • Gender and Leadership Roles : Men are more likely to hold leadership positions in corporate settings.
  • Social Support and Mental Health : Strong social support networks reduce the risk of depression.
  • Quality of Sleep and Productivity : Better sleep quality leads to higher productivity levels.
  • High-Fat Diet and Cholesterol Levels : A high-fat diet increases cholesterol levels.
  • Caffeine Intake and Alertness : Higher caffeine intake enhances alertness and cognitive function.
  • Online Shopping Habits : People who frequently shop online spend more money than in-store shoppers. …
  • Education and Political Views : Higher education levels are associated with more liberal political views.
  • Gender and Risk-Taking Behavior : Men are more likely to engage in risky behaviors.
  • Temperature and Ice Cream Sales : Higher temperatures increase ice cream sales.
  • Artificial Sweeteners and Weight Loss : Consuming products with artificial sweeteners aids in weight loss.
  • Exercise and Stress Reduction : Regular exercise reduces stress levels.
  • Music Genres and Mood : Listening to upbeat music improves mood.
  • Online Learning and Engagement : Online learners are more engaged in virtual classroom discussions.
  • Personality Traits and Job Performance : Extroverted individuals perform better in sales roles.
  • Environmental Awareness and Recycling : Higher environmental awareness leads to more recycling practices.
  • Social Media Usage and Self-Esteem : Excessive social media usage correlates with lower self-esteem. …
  • Sleep Deprivation and Reaction Time : Sleep-deprived individuals have slower reaction times.
  • Breakfast Consumption and Metabolism : Eating breakfast kickstarts metabolism for the day.
  • Leadership Style and Employee Satisfaction : Transformational leadership style increases employee job satisfaction.
  • Bilingualism and Cognitive Abilities : Bilingual individuals possess enhanced cognitive abilities.
  • Video Game Playing and Aggression : Playing violent video games increases aggressive behavior.
  • Hydration and Cognitive Function : Staying hydrated improves cognitive function.
  • Parental Support and Academic Achievement : Supportive parenting leads to higher academic achievement.
  • Workplace Flexibility and Work-Life Balance : Jobs with flexible schedules enhance work-life balance.
  • Digital Learning and Knowledge Retention : Digital learning methods improve long-term knowledge retention.
  • Art Exposure and Creativity : Exposure to various forms of art fosters creative thinking.
  • Solar Energy Adoption and Utility Bills : Homes with solar energy systems experience lower utility bills.
  • Parental Involvement and Student Behavior : Increased parental involvement reduces student behavioral issues.
  • Team Diversity and Creativity : Diverse teams generate more creative solutions.
  • Social Media Marketing and Brand Awareness : Social media marketing boosts brand awareness more than traditional methods.
  • Morning Routine and Productivity : Following a structured morning routine enhances overall productivity.
  • Music Training and Cognitive Development : Music training improves cognitive abilities in children.
  • Employee Training and Job Satisfaction : Comprehensive employee training programs lead to higher job satisfaction.
  • Eating Before Bed and Sleep Quality : Consuming heavy meals before bed negatively affects sleep quality.
  • Financial Incentives and Employee Performance : Offering financial incentives increases employee performance.
  • Parental Attachment and Emotional Well-being : Strong parental attachment fosters better emotional well-being in children.
  • Social Interaction and Mental Well-being : Frequent social interaction correlates with improved mental health.
  • Education and Crime Rates : Higher education levels result in lower crime rates within communities.
  • Diet and Acne : A diet high in dairy products exacerbates acne.
  • Leadership Style and Employee Motivation : Autocratic leadership style hampers employee motivation.
  • Urban Green Spaces and Stress Reduction : Access to urban green spaces lowers stress levels.
  • Sleep Duration and Athletic Performance : Adequate sleep duration enhances athletic performance.
  • Financial Literacy and Investment Success : Individuals with high financial literacy make more successful investments.
  • Team Collaboration and Project Success : Effective team collaboration leads to more successful project outcomes.
  • Media Exposure and Body Image : Increased media exposure contributes to negative body image perceptions.
  • Gender Representation and Film Success : Movies with more balanced gender representation achieve higher box office success. …
  • Meditation and Anxiety Reduction : Regular meditation practice reduces symptoms of anxiety.
  • Cognitive Training and Memory Enhancement : Cognitive training programs improve memory retention.
  • Positive Affirmations and Self-Confidence : Repeating positive affirmations enhances self-confidence.
  • Physical Fitness and Longevity : Being physically fit is linked to increased lifespan.
  • Parental Guidance and Online Safety : Strong parental guidance promotes responsible online behavior in children.
  • Artificial Intelligence and Job Displacement : Increased AI integration leads to more job displacement.
  • Public Transportation Usage and Air Quality : Increased public transportation usage improves air quality in cities.
  • Social Support and Addiction Recovery : Strong social support networks aid in addiction recovery.
  • Gender Diversity and Company Performance : Companies with diverse gender representation outperform others.
  • Mindfulness Meditation and Pain Management : Mindfulness meditation reduces perception of pain.
  • Music Therapy and Autism : Music therapy improves social interaction skills in children with autism.
  • Social Media Usage and Academic Performance : Excessive social media usage negatively impacts academic performance.
  • Employee Engagement and Organizational Success : Higher employee engagement leads to greater organizational success.
  • Healthy Eating and Longevity : A diet rich in fruits and vegetables contributes to a longer lifespan.
  • Gender Stereotypes and Career Choice : Gender stereotypes influence career choices among young adults.
  • Environmental Conservation Efforts and Biodiversity : Increased conservation efforts positively affect biodiversity.
  • Volunteerism and Personal Well-being : Engaging in volunteer activities enhances personal well-being.
  • Artificial Intelligence and Customer Service : AI-driven customer service improves user satisfaction.

Alternative Hypothesis Statement Examples in Research

In alternative research hypothesis propel investigations beyond the null. Examples span diverse fields, revealing the direction researchers expect their findings to take.

  • Effect of Music on Concentration : Listening to classical music enhances concentration during study.
  • Green Tea and Weight Loss : Green tea consumption leads to more significant weight loss than water intake.
  • Parental Involvement and Academic Achievement : Active parental involvement boosts student academic achievement.
  • Social Media Usage and Self-Esteem : Frequent social media use correlates with lower self-esteem.

Alternative Hypothesis Statement Examples in Business Research

Business research thrives on alternative hypotheses. Dive into these business-oriented examples that challenge null assumptions.

  • Marketing Campaign Impact : Marketing campaign A generates higher conversion rates than campaign B.
  • Employee Training and Productivity : Comprehensive employee training enhances workplace productivity.
  • Work-Life Balance and Employee Satisfaction : Improved work-life balance increases employee job satisfaction.
  • Customer Service Channel Effectiveness : Online chat support results in higher customer satisfaction compared to phone support.
  • Branding Influence on Purchase Intent : Strong brand presence leads to increased purchase intent.

Directional Alternative Hypothesis Statement Examples

Directional hypothesis add clarity to research expectations. Explore these examples that predict specific outcomes.

  • Exercise Frequency and Heart Health : Engaging in physical activity five times a week improves heart health.

Alternative Hypothesis Statement Examples in Psychology

Psychological studies benefit from well-crafted alternative hypotheses. These psychology hypothesis examples delve into the realm of human behavior and cognition.

  • Mindfulness Meditation and Anxiety Reduction : Regular mindfulness practice reduces symptoms of anxiety.

Alternative Null Hypothesis Statement Examples

Explore alternative null hypothesis —statements asserting the absence of specific effects or differences.

  • Coffee Consumption and Weight Gain : Increased coffee consumption does not lead to weight gain.
  • Smartphone Usage and Sleep Quality : Using smartphones before bed does not impact sleep quality.
  • Music Genre and Study Performance : Studying with rock music does not affect academic performance.
  • Green Spaces and Stress Reduction : Access to green spaces does not decrease stress levels.
  • Team Diversity and Project Success : Team diversity does not influence project success rates.

Alternative Hypothesis Statement Examples in Medical Research

Medical research relies on robust alternative hypotheses to drive scientific inquiry. These examples explore hypotheses in the realm of healthcare.

  • Exercise and Diabetes Prevention : Regular exercise decreases the risk of developing type 2 diabetes.
  • Medication A and Blood Pressure Reduction : Medication A leads to greater reduction in blood pressure compared to medication B.
  • Nutritional Intake and Heart Disease : Higher intake of fruits and vegetables lowers the risk of heart disease.
  • Stress Reduction Techniques and Anxiety Levels : Practicing stress reduction techniques decreases anxiety levels.
  • Alternative Medicine and Pain Management : Alternative medicine therapies alleviate chronic pain more effectively than traditional treatments.

Alternative Hypothesis Statement Examples in Education Research

Education research thrives on alternative hypotheses to investigate innovative approaches. Explore examples that challenge conventional notions.

  • Technology Integration and Student Engagement : Integrating technology enhances student engagement in the classroom.
  • Project-Based Learning and Knowledge Retention : Project-based learning improves long-term knowledge retention.
  • Teacher Professional Development and Student Performance : Effective teacher professional development positively impacts student academic performance.
  • Inclusive Classroom Environment and Learning Outcomes : Inclusive classrooms lead to better learning outcomes for diverse students.
  • Feedback Frequency and Writing Improvement : Frequent feedback results in greater improvement in student writing skills.

These examples showcase the pivotal role of alternative hypotheses across various disciplines, serving as the driving force behind scientific exploration and advancement.

What is the Alternative Hypothesis Formula?

The alternative hypothesis, denoted as “Ha” or “H1,” represents the assertion researchers aim to support through evidence. It stands in contrast to the null hypothesis (Ho), which suggests no effect or relationship. The formula for the alternative hypothesis varies based on the nature of the study:

  • Directional Hypothesis : For studies with an expected direction, the formula takes the form of a prediction. For instance, “The new drug increases patient recovery rates.”
  • Non-Directional Hypothesis : For exploratory studies, the formula reflects the possibility of any difference or effect. For example, “There is a difference in recovery rates between the two drugs.”

How do you start an Alternative Hypothesis?

Starting an alternative simple hypothesis involves framing a clear research statement that highlights the anticipated effect, relationship, or difference. To begin:

  • Identify the Research Question: Determine the specific aspect you intend to explore or compare.
  • Formulate a Hypothesis: Craft a statement that directly addresses the expected outcome.
  • Include Variables: Introduce the relevant variables and their predicted connection.
  • Be Clear and Specific: Ensure the alternative hypothesis is concise and unambiguous.

Is the Alternative Hypothesis a Claim or Statement?

The alternative hypothesis is both a claim and a statement. It claims that there is a measurable effect, relationship, or difference in the variables being studied. It is also a statement that researchers work to validate through evidence.

How do you write an Alternative Hypothesis Statement? – Step by Step Guide

Creating a robust alternative hypothesis statement involves structured steps:

  • Identify Variables : Clearly define the independent and dependent variables in your study.
  • State Expected Effect : Express the anticipated impact, relationship, or difference between variables.
  • Be Precise : Use specific language to convey the exact nature of the expected outcome.
  • Include Direction (if applicable) : If your hypothesis is directional, specify the expected direction.
  • Avoid Ambiguity : Make sure your statement is clear and leaves no room for confusion.

Tips for Writing an Alternative Hypothesis Statement

  • Be Specific : Clearly define the variables and the predicted relationship.
  • Use Measurable Terms : Incorporate quantifiable terms to indicate the magnitude of the effect.
  • Testability : Ensure the hypothesis can be tested empirically.
  • Conciseness : Keep the statement concise and to the point.
  • Alignment with Research Question : Ensure the hypothesis directly answers your research question.
  • Avoid Value Judgments : Avoid value judgments or personal biases in the hypothesis.
  • Review Literature : Consult existing literature to align your hypothesis with prior research.

Crafting a strong alternative hypothesis statement is essential for guiding your research and forming the basis for causual hypothesis testing. It directs the focus of your investigation and lays the foundation for drawing meaningful conclusions.

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  1. Hypothesis Testing: the null and alternative hypotheses

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  6. NEGATIVE RESEARCH HYPOTHESIS STATEMENTS l 3 EXAMPLES l RESEARCH PAPER WRITING GUIDE l THESIS TIPS

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  1. Null & Alternative Hypotheses

    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 (H0): There's no effect in the population. Alternative hypothesis (Ha or H1): There's an effect in the population. The effect is usually the effect of the ...

  2. 17 Examples of an Alternative Hypothesis

    The following are hypothetical examples of an alternative hypothesis.Years of kendo experience has a positive correlation with personal resilience.Coffee drinkers have higher average productivity than people who don't drink coffee.Temperature influences the volume of alcohol.Rain causes mud puddles.There is a positive correlation between the ...

  3. 9.2: 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.

  4. 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.

  5. 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 ...

  6. 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.

  7. 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.

  8. 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.

  9. Alternative hypothesis

    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. In other words, we must ensure that. Example As in the previous example, consider a test about the mean of a normal distribution, where we test .

  10. How to Write a Strong Hypothesis

    Developing a hypothesis (with example) Step 1. Ask a question. Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question.

  11. Alternative hypothesis

    The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making judgments on the basis of data. In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements. "The statement being tested in a test of statistical significance is called the null ...

  12. 5.2

    5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the ...

  13. 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 ...

  14. 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 ...

  15. Alternative Hypothesis in Statistics

    The alternative hypothesis is a hypothesis used in significance testing which contains a strict inequality. A test of significance will result in either rejecting the null hypothesis (indicating ...

  16. Null & Alternative Hypotheses

    The null hypothesis is a presumption of status quo or no change. Alternative Hypothesis (Ha) - 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:H0: There is no difference in the salary of factory ...

  17. Alternative Hypothesis-Definition, Types and Examples

    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. ... Example. To check the water quality of a river for one year, the researchers are doing the observation. As per the null ...

  18. 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. Let us discuss what an alternative hypothesis is, how it is different from the null hypothesis, its types, and some examples in our article.

  19. What Is an Alternative Hypothesis? (Definition and Examples)

    A null hypothesis is a statement you try to reject, which means a null assumes something is true. For example, a null hypothesis may say that temperature has no impact on crime rates in a certain city. The alternative hypothesis assumes this is false, meaning it may claim the weather has a positive or negative impact on crime rates.

  20. Alternative Hypothesis: Definition, Types and Examples

    1. One-tailed test H1: 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. 2. Two-tailed test H1: A two-tailed alternative hypothesis is concerned with both regions of rejection of the sampling distribution. 3.

  21. Alternative Hypothesis

    Often contrasted with a null hypothesis, it indicates the expected direction of the tested relation. Dive into these varied thesis statement examples showcasing the core essence of alternative hypotheses. Smoking and Cancer: Smoking is positively related to lung cancer incidence. Diet and Weight Loss: The Atkins diet results in more weight loss ...

  22. How to Write a Null Hypothesis (5 Examples)

    Example 1: Weight of Turtles. A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles. Here is how to write the null and alternative hypotheses for this scenario: H0: μ = 300 (the true mean weight is equal to ...