null hypothesis question example

15 Null Hypothesis Examples

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

Learn about our Editorial Process

null hypothesis example and definition, explained below

A null hypothesis is a general assertion or default position that there is no relationship or effect between two measured phenomena.

It’s a critical part of statistics, data analysis, and the scientific method . This concept forms the basis of testing statistical significance and allows researchers to be objective in their conclusions.

A null hypothesis helps to eliminate biases and ensures that the observed results are not due to chance. The rejection or failure to reject the null hypothesis helps in guiding the course of research.

Null Hypothesis Definition

The null hypothesis, often denoted as H 0 , is the hypothesis in a statistical test which proposes no statistical significance exists in a set of observed data.

It hypothesizes that any kind of difference or importance you see in a data set is due to chance.

Null hypotheses are typically proposed to be negated or disproved by statistical tests, paving way for the acceptance of an alternate hypothesis.

Importantly, a null hypothesis cannot be proven true; it can only be supported or rejected with confidence.

Should evidence – via statistical analysis – contradict the null hypothesis, it is rejected in favor of an alternative hypothesis. In essence, the null hypothesis is a tool to challenge and disprove that there is no effect or relationship between variables.

Video Explanation

I like to show this video to my students which outlines a null hypothesis really clearly and engagingly, using real life studies by research students! The into explains it really well:

“There’s an idea in science called the null hypothesis and it works like this: when you’re setting out to prove a theory, your default answer should be “it’s not going to work” and you have to convince the world otherwise through clear results”

Here’s the full video:

Null Hypothesis Examples

Equality of Means: The null hypothesis posits that the average of group A does not differ from the average of group B. It suggests that any observed difference between the two group means is due to sampling or experimental error.
No Correlation: The null hypothesis states there is no correlation between the variable X and variable Y in the population. It means that any correlation seen in sample data occurred by chance.
Drug Effectiveness: The null hypothesis proposes that a new drug does not reduce the number of days to recover from a disease compared to a standard drug. Any observed difference is merely by chance and not due to the new drug.
Classroom Teaching Method: The null hypothesis states that a new teaching method does not result in improved test scores compared to the traditional teaching method. Any improvement in scores can be attributed to chance or other unrelated factors.
Smoking and Life Expectancy: The null hypothesis asserts that the average life expectancy of smokers is the same as that of non-smokers. Any perceived difference in life expectancy is due to random variation or other factors.
Brand Preference: The null hypothesis suggests that the proportion of consumers preferring Brand A is the same as those preferring Brand B. Any observed preference in the sample is due to random selection.
Vaccination Efficacy: The null hypothesis states that the efficacy of Vaccine A does not differ from that of Vaccine B. Any differences observed in a sample are due to chance or other confounding factors.
Diet and Weight Loss: The null hypothesis proposes that following a specific diet does not result in more weight loss than not following the diet. Any weight loss observed among dieters is considered random or influenced by other factors.
Exercise and Heart Rate: The null hypothesis states that regular exercise does not lower resting heart rate compared to no exercise. Any lower heart rates observed in exercisers could be due to chance or other unrelated factors.
Climate Change: The null hypothesis asserts that the average global temperature this decade is not higher than the previous decade. Any observed temperature increase can be attributed to random variation or unaccounted factors.
Gender Wage Gap: The null hypothesis posits that men and women earn the same average wage for the same job. Any observed wage disparity is due to chance or non-gender related factors.
Psychotherapy Effectiveness: The null hypothesis states that patients undergoing psychotherapy do not show more improvement than those not undergoing therapy. Any improvement in the
Energy Drink Consumption and Sleep: The null hypothesis proposes that consuming energy drinks does not affect the quantity of sleep. Any observed differences in sleep duration among energy drink consumers is due to random variation or other factors.
Organic Food and Health: The null hypothesis asserts that consuming organic food does not lead to better health outcomes compared to consuming non-organic food. Any health differences observed in consumers of organic food are considered random or attributed to other confounding factors.
Online Learning Effectiveness: The null hypothesis states that students learning online do not perform differently on exams than students learning in traditional classrooms. Any difference in performance can be attributed to chance or unrelated factors.

Null Hypothesis vs Alternative Hypothesis

An alternative hypothesis is the direct contrast to the null hypothesis. It posits that there is a statistically significant relationship or effect between the variables being observed.

If the null hypothesis is rejected based on the test data, the alternative hypothesis is accepted.

Importantly, while the null hypothesis is typically a statement of ‘no effect’ or ‘no difference,’ the alternative hypothesis states that there is an effect or difference.

Comprehension Checkpoint: How does the null hypothesis help to ensure that research is objective and unbiased?

Applications of the Null Hypothesis in Research

The null hypothesis plays a critical role in numerous research settings, promoting objectivity and ensuring findings aren’t due to random chance.

Clinical Trials: Null hypothesis is used extensively in medical and pharmaceutical research. For example, when testing a new drug’s effectiveness, the null hypothesis might state that the drug has no effect on the disease. If data contradicts this, the null hypothesis is rejected, suggesting the drug might be effective.
Business and Economics: Businesses use null hypotheses to make informed decisions. For instance, a company might use a null hypothesis to test if a new marketing strategy improves sales. If data suggests a significant increase in sales, the null hypothesis is rejected, and the new strategy may be implemented.
Psychological Research: Psychologists use null hypotheses to test theories about behavior. For instance, a null hypothesis might state there’s no link between stress and sleep quality. Rejecting this hypothesis based on collected data could help establish a correlation between the two variables.
Environmental Science: Null hypotheses are used to understand environmental changes. For instance, researchers might form a null hypothesis stating there is no significant difference in air quality before and after a policy change. If this hypothesis is rejected, it indicates the policy may have impacted air quality.
Education: Educators and researchers often use null hypotheses to improve teaching methods. For example, a null hypothesis might propose a new teaching technique doesn’t enhance student performance. If data contradicts this, the technique may be beneficial.

In all these areas, the null hypothesis helps minimize bias, enabling researchers to support their findings with statistically significant data. It forms the backbone of many scientific research methodologies , promoting a disciplined approach to uncovering new knowledge.

See More Hypothesis Examples Here

The null hypothesis is a cornerstone of statistical analysis and empirical research. It serves as a starting point for investigations, providing a baseline premise that the observed effects are due to chance. By understanding and applying the concept of the null hypothesis, researchers can test the validity of their assumptions, making their findings more robust and reliable. In essence, the null hypothesis ensures that the scientific exploration remains objective, systematic, and free from unintended bias.

Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ Free Social Skills Worksheets
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 10 Reasons you’re Perpetually Single
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 20 Montessori Toddler Bedrooms (Design Inspiration)
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 21 Montessori Homeschool Setups

Null Hypothesis Examples

ThoughtCo / Hilary Allison

Scientific Method
Chemical Laws
Periodic Table
Projects & Experiments
Biochemistry
Physical Chemistry
Medical Chemistry
Chemistry In Everyday Life
Famous Chemists
Activities for Kids
Abbreviations & Acronyms
Weather & Climate
Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
B.A., Physics and Mathematics, Hastings College

In statistical analysis, the null hypothesis assumes there is no meaningful relationship between two variables. Testing the null hypothesis can tell you whether your results are due to the effect of manipulating a dependent variable or due to chance. It's often used in conjunction with an alternative hypothesis, which assumes there is, in fact, a relationship between two variables.

The null hypothesis is among the easiest hypothesis to test using statistical analysis, making it perhaps the most valuable hypothesis for the scientific method. By evaluating a null hypothesis in addition to another hypothesis, researchers can support their conclusions with a higher level of confidence. Below are examples of how you might formulate a null hypothesis to fit certain questions.

What Is the Null Hypothesis?

The null hypothesis states there is no relationship between the measured phenomenon (the dependent variable ) and the independent variable , which is the variable an experimenter typically controls or changes. You do not need to believe that the null hypothesis is true to test it. On the contrary, you will likely suspect there is a relationship between a set of variables. One way to prove that this is the case is to reject the null hypothesis. Rejecting a hypothesis does not mean an experiment was "bad" or that it didn't produce results. In fact, it is often one of the first steps toward further inquiry.

To distinguish it from other hypotheses , the null hypothesis is written as H 0 (which is read as “H-nought,” "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95% or 99% is common. Keep in mind, even if the confidence level is high, there is still a small chance the null hypothesis is not true, perhaps because the experimenter did not account for a critical factor or because of chance. This is one reason why it's important to repeat experiments.

Examples of the Null Hypothesis

To write a null hypothesis, first start by asking a question. Rephrase that question in a form that assumes no relationship between the variables. In other words, assume a treatment has no effect. Write your hypothesis in a way that reflects this.

Other Types of Hypotheses

In addition to the null hypothesis, the alternative hypothesis is also a staple in traditional significance tests . It's essentially the opposite of the null hypothesis because it assumes the claim in question is true. For the first item in the table above, for example, an alternative hypothesis might be "Age does have an effect on mathematical ability."

Key Takeaways

In hypothesis testing, the null hypothesis assumes no relationship between two variables, providing a baseline for statistical analysis.
Rejecting the null hypothesis suggests there is evidence of a relationship between variables.
By formulating a null hypothesis, researchers can systematically test assumptions and draw more reliable conclusions from their experiments.
What Are Examples of a Hypothesis?
Random Error vs. Systematic Error
Six Steps of the Scientific Method
What Is a Hypothesis? (Science)
Scientific Method Flow Chart
What Are the Elements of a Good Hypothesis?
Scientific Method Vocabulary Terms
Understanding Simple vs Controlled Experiments
The Role of a Controlled Variable in an Experiment
What Is an Experimental Constant?
What Is a Testable Hypothesis?
Scientific Hypothesis Examples
What Is the Difference Between a Control Variable and Control Group?
DRY MIX Experiment Variables Acronym
What Is a Controlled Experiment?
Scientific Variable

Mathematics
Number System and Arithmetic
Trigonometry
Probability
Mensuration

Null Hypothesis

Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.

In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.

Table of Content

What is Null Hypothesis?

Null hypothesis symbol, formula of null hypothesis, types of null hypothesis, null hypothesis examples, principle of null hypothesis, how do you find null hypothesis, null hypothesis in statistics, null hypothesis and alternative hypothesis, null hypothesis and alternative hypothesis examples, null hypothesis - practice problems.

Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply "null," it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.

Null Hypothesis Meaning

Null Hypothesis represents a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.

The null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.

Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.

The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.

Mean Comparison (Two-sample t-test)

H 0 : μ 1 = μ 2

This asserts that there is no significant difference between the means of two populations or groups.

Proportion Comparison

H 0 : p 1 − p 2 = 0

This suggests no significant difference in proportions between two populations or conditions.

Equality in Variance (F-test in ANOVA)

H 0 : σ 1 = σ 2

This states that there's no significant difference in variances between groups or populations.

Independence (Chi-square Test of Independence):

H 0 : Variables are independent

This asserts that there's no association or relationship between categorical variables.

Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.

Equality Null Hypothesis (Simple Null Hypothesis)

The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.

Non-Inferiority Null Hypothesis

In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.

Superiority Null Hypothesis

The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.

Independence Null Hypothesis

In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.

Homogeneity Null Hypothesis

In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there's no difference in population means across different groups.

Medicine: Null Hypothesis: "No significant difference exists in blood pressure levels between patients given the experimental drug versus those given a placebo."
Education: Null Hypothesis: "There's no significant variation in test scores between students using a new teaching method and those using traditional teaching."
Economics: Null Hypothesis: "There's no significant change in consumer spending pre- and post-implementation of a new taxation policy."
Environmental Science: Null Hypothesis: "There's no substantial difference in pollution levels before and after a water treatment plant's establishment."

The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.

In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.

The null hypothesis is usually formulated to be tested against an alternative hypothesis (H 1 or H \alpha ) which suggests that there is an effect, difference or relationship present in the population.

Null Hypothesis Rejection

Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.

When is Null Hypothesis Rejected?

The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

In statistical hypothesis testing, researchers begin by stating the null hypothesis, often based on theoretical considerations or previous research. The null hypothesis is then tested against an alternative hypothesis (Ha), which represents the researcher's claim or the hypothesis they seek to support.

The process of hypothesis testing involves collecting sample data and using statistical methods to assess the likelihood of observing the data if the null hypothesis were true. This assessment is typically done by calculating a test statistic, which measures the difference between the observed data and what would be expected under the null hypothesis.

In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.

Difference Between Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher's intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.

Let's envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:

Null Hypothesis (H 0 ): "The new medication does not produce a significant effect in reducing blood pressure levels among patients."

Alternative Hypothesis (H 1 or Ha): "The new medication yields a significant effect in reducing blood pressure levels among patients."

The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication's administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.

Summary - Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) and alternative hypothesis (H a ) are fundamental concepts in statistical hypothesis testing. The null hypothesis represents the default assumption, stating that there is no significant effect, difference, or relationship between variables. It serves as the baseline against which the alternative hypothesis is tested. In contrast, the alternative hypothesis represents the researcher's hypothesis or the claim to be tested, suggesting that there is a significant effect, difference, or relationship between variables. The relationship between the null and alternative hypotheses is such that they are complementary, and statistical tests are conducted to determine whether the evidence from the data is strong enough to reject the null hypothesis in favor of the alternative hypothesis. This decision is based on the strength of the evidence and the chosen level of significance. Ultimately, the choice between the null and alternative hypotheses depends on the specific research question and the direction of the effect being investigated.

FAQs on Null Hypothesis

What does null hypothesis stands for.

The null hypothesis, denoted as H 0 , is a fundamental concept in statistics used for hypothesis testing. It represents the statement that there is no effect or no difference, and it is the hypothesis that the researcher typically aims to provide evidence against.

How to Form a Null Hypothesis?

A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.

When Do we reject the Null Hypothesis?

In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.

What is a Null Hypothesis in Research?

In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.

What Are Alternative and Null Hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.

What Does it Mean to Reject the Null Hypothesis?

Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.

How to Find Null Hypothesis?

Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.

How is Null Hypothesis denoted?

The null hypothesis is commonly symbolized as H 0 in statistical notation.

What is the Purpose of the Null hypothesis in Statistical Analysis?

The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there's enough evidence to reject it in favor of an alternative hypothesis.

What happens if we Reject the Null hypothesis?

Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.

What are Test for Null Hypothesis?

Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

User Preferences

Content preview.

Arcu felis bibendum ut tristique et egestas quis:

Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris
Duis aute irure dolor in reprehenderit in voluptate
Excepteur sint occaecat cupidatat non proident

Keyboard Shortcuts

10.1 - setting the hypotheses: examples.

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

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

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

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

State Null and Alternative Hypotheses

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Calculation of a person's approximate tip for their meal

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

Science Notes Posts
Contact Science Notes
Todd Helmenstine Biography
Anne Helmenstine Biography
Free Printable Periodic Tables (PDF and PNG)
Periodic Table Wallpapers
Interactive Periodic Table
Periodic Table Posters
Science Experiments for Kids
How to Grow Crystals
Chemistry Projects
Fire and Flames Projects
Holiday Science
Chemistry Problems With Answers
Physics Problems
Unit Conversion Example Problems
Chemistry Worksheets
Biology Worksheets
Periodic Table Worksheets
Physical Science Worksheets
Science Lab Worksheets
My Amazon Books

Null Hypothesis Examples

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

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

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

What Is the Null Hypothesis?

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

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

Exact and Inexact Null Hypothesis

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

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

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

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

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

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

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

How to State the Null Hypothesis

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

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

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

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

H A : μ < 3

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

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

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

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

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

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

Math Article

Null Hypothesis

In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.

Table of contents:

Comparison with Alternative Hypothesis

Null Hypothesis Definition

The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .

Null Hypothesis Symbol

In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .

Null Hypothesis Principle

The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.

Null Hypothesis Formula

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

H 0 : p = p 0

The formula for the alternative hypothesis is:

H a = p >p 0 , < p 0 ≠ p 0

The formula for the test static is:

Remember that, p 0 is the null hypothesis and p – hat is the sample proportion.

Also, read:

Types of Null Hypothesis

There are different types of hypothesis. They are:

Simple Hypothesis

It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.

Composite Hypothesis

The composite hypothesis is one that does not completely specify the population distribution.

Exact Hypothesis

Exact hypothesis defines the exact value of the parameter. For example μ= 50

Inexact Hypothesis

This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60

Null Hypothesis Rejection

Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.

How do you Find the Null Hypothesis?

The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).

When is Null Hypothesis Rejected?

The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.

Null Hypothesis and Alternative Hypothesis

Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.

Null Hypothesis Examples

Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.

If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.

Few more examples are:

1). Are there is 100% chance of getting affected by dengue?

Ans: There could be chances of getting affected by dengue but not 100%.

2). Do teenagers are using mobile phones more than grown-ups to access the internet?

Ans: Age has no limit on using mobile phones to access the internet.

3). Does having apple daily will not cause fever?

Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.

4). Do the children more good in doing mathematical calculations than grown-ups?

Ans: Age has no effect on Mathematical skills.

In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives.

The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data.

Frequently Asked Questions on Null Hypothesis

What is meant by the null hypothesis.

In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

What are the benefits of hypothesis testing?

Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.

When a null hypothesis is accepted and rejected?

The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.

Why is the null hypothesis important?

The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.

How to accept or reject the null hypothesis in the chi-square test?

If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Maths related queries and study materials

Your result is as below

Request OTP on Voice Call

Register with BYJU'S & Download Free PDFs

Have a thesis expert improve your writing

Check your thesis for plagiarism in 10 minutes, generate your apa citations for free.

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 .

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.

Cite this Scribbr article

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

Turney, S. (2022, December 06). Null and Alternative Hypotheses | Definitions & Examples. Scribbr. Retrieved 16 December 2024, from https://www.scribbr.co.uk/stats/null-and-alternative-hypothesis/

Is this article helpful?

Shaun Turney

Other students also liked, levels of measurement: nominal, ordinal, interval, ratio, the standard normal distribution | calculator, examples & uses, types of variables in research | definitions & examples.

Null Hypothesis

Ai generator.

Making a certain class or laboratory experiment would require a good null hypothesis . You will be given variables to be used in your experiment and then you would be able to identify the relationship between the two. Every beginning of the experiment report would indicate your hypotheses. It is proven useful for it can be tested to prove if the result is considered false.

What is a Null Hypothesis?

A null hypothesis is used during experiments to prove that there is no difference in the relationship between the two variables. Every type of experiment would require you to make a null hypothesis. From the word itself “null” means zero or no value. If you want to practice making a good experiment report , consider providing a good null hypothesis. Null hypothesis is designed to be rejected if the alternative hypothesis is proven to be exact.

Null Hypothesis Examples in Research

1. medical research.

Research Question: Does a new drug lower cholesterol levels more effectively than the current drug?
Null Hypothesis (H0): The new drug has no effect on cholesterol levels compared to the current drug.
Symbolic Form: H0: ?1 = ?2

2. Educational Research

Research Question: Does the use of interactive technology improve student test scores?
Null Hypothesis (H0): Interactive technology does not improve student test scores.

3. Business Research

Research Question: Does a new marketing strategy increase sales?
Null Hypothesis (H0): The new marketing strategy does not increase sales.

4. Psychological Research

Research Question: Does cognitive-behavioral therapy reduce symptoms of anxiety more than standard therapy?
Null Hypothesis (H0): Cognitive-behavioral therapy does not reduce anxiety symptoms more than standard therapy.

5. Environmental Research

Research Question: Does urbanization affect bird population diversity?
Null Hypothesis (H0): Urbanization has no effect on bird population diversity.
Symbolic Form: H0: ?urban = ?rural

6. Nutritional Research

Research Question: Does a low-carb diet lead to more weight loss than a low-fat diet?
Null Hypothesis (H0): A low-carb diet does not lead to more weight loss than a low-fat diet.

7. Economic Research

Research Question: Does increasing the minimum wage reduce poverty levels?
Null Hypothesis (H0): Increasing the minimum wage does not reduce poverty levels.
Symbolic Form: H0: ?before = ?after

8. Sociological Research

Research Question: Does social media usage affect teenagers’ self-esteem?
Null Hypothesis (H0): Social media usage does not affect teenagers’ self-esteem.
Symbolic Form: H0: ?users = ?non-users

9. Agricultural Research

Research Question: Does the use of a new fertilizer increase crop yield?
Null Hypothesis (H0): The new fertilizer does not increase crop yield.

10. Technological Research

Research Question: Does a new software algorithm improve processing speed?
Null Hypothesis (H0): The new software algorithm does not improve processing speed.
Symbolic Form: H0: ?new = ?old

Null Hypothesis Examples in Psychology

1. effectiveness of therapy.

Research Question: Does cognitive-behavioral therapy (CBT) reduce symptoms of depression more effectively than no treatment?
Null Hypothesis (H0): Cognitive-behavioral therapy does not reduce symptoms of depression more effectively than no treatment.
Symbolic Form: H0: ?CBT = ?control

2. Impact of Sleep on Memory

Research Question: Does sleep deprivation affect short-term memory performance?
Null Hypothesis (H0): Sleep deprivation has no effect on short-term memory performance.
Symbolic Form: H0: ?sleep_deprived = ?non_sleep_deprived

3. Influence of Color on Mood

Research Question: Does the color of a room affect individuals’ mood?
Null Hypothesis (H0): The color of a room does not affect individuals’ mood.
Symbolic Form: H0: ?color1 = ?color2 = ?color3

4. Social Media and Self-Esteem

Research Question: Does the frequency of social media use affect teenagers’ self-esteem?
Null Hypothesis (H0): The frequency of social media use does not affect teenagers’ self-esteem.
Symbolic Form: H0: ?high_use = ?low_use

5. Mindfulness and Stress Reduction

Research Question: Does mindfulness meditation reduce stress levels in college students?
Null Hypothesis (H0): Mindfulness meditation does not reduce stress levels in college students.
Symbolic Form: H0: ?mindfulness = ?control

6. Parenting Styles and Academic Performance

Research Question: Does authoritative parenting style affect children’s academic performance?
Null Hypothesis (H0): Authoritative parenting style does not affect children’s academic performance.
Symbolic Form: H0: ?authoritative = ?other_styles

7. Impact of Exercise on Anxiety

Research Question: Does regular exercise reduce anxiety levels in adults?
Null Hypothesis (H0): Regular exercise does not reduce anxiety levels in adults.
Symbolic Form: H0: ?exercise = ?no_exercise

8. Gender Differences in Risk-Taking Behavior

Research Question: Are there differences in risk-taking behavior between males and females?
Null Hypothesis (H0): There are no differences in risk-taking behavior between males and females.
Symbolic Form: H0: ?males = ?females

9. Impact of Music on Concentration

Research Question: Does listening to music while studying affect concentration levels?
Null Hypothesis (H0): Listening to music while studying does not affect concentration levels.
Symbolic Form: H0: ?music = ?no_music

10. Effect of Group Therapy on Social Skills

Research Question: Does group therapy improve social skills in individuals with social anxiety?
Null Hypothesis (H0): Group therapy does not improve social skills in individuals with social anxiety.
Symbolic Form: H0: ?group_therapy = ?no_therapy

Null Hypothesis Examples in Biology

1. effect of fertilizers on plant growth.

Research Question: Does a new fertilizer improve plant growth compared to no fertilizer?
Null Hypothesis (H0): The new fertilizer does not improve plant growth compared to no fertilizer.
Symbolic Form: H0: ?fertilizer = ?no_fertilizer

2. Antibiotic Effectiveness on Bacteria

Research Question: Does a new antibiotic reduce bacterial growth more effectively than an existing antibiotic?
Null Hypothesis (H0): The new antibiotic does not reduce bacterial growth more effectively than the existing antibiotic.
Symbolic Form: H0: ?new_antibiotic = ?existing_antibiotic

3. Impact of Temperature on Enzyme Activity

Research Question: Does temperature affect the activity of a specific enzyme?
Null Hypothesis (H0): Temperature does not affect the activity of the specific enzyme.
Symbolic Form: H0: Enzyme activity at temperature1 = Enzyme activity at temperature2

4. Genetic Influence on Trait Expression

Research Question: Does a specific gene affect the expression of a particular trait in a plant species?
Null Hypothesis (H0): The specific gene does not affect the expression of the particular trait in the plant species.
Symbolic Form: H0: Trait expression with gene = Trait expression without gene

5. Effect of Light Intensity on Photosynthesis

Research Question: Does light intensity affect the rate of photosynthesis in plants?
Null Hypothesis (H0): Light intensity does not affect the rate of photosynthesis in plants.
Symbolic Form: H0: Photosynthesis rate at light intensity1 = Photosynthesis rate at light intensity2

6. Impact of Diet on Animal Growth

Research Question: Does a high-protein diet affect the growth rate of animals?
Null Hypothesis (H0): A high-protein diet does not affect the growth rate of animals.
Symbolic Form: H0: Growth rate on high-protein diet = Growth rate on normal diet

7. Effect of Pollution on Aquatic Life

Research Question: Does water pollution affect the survival rate of fish in a lake?
Null Hypothesis (H0): Water pollution does not affect the survival rate of fish in a lake.
Symbolic Form: H0: Fish survival in polluted water = Fish survival in non-polluted water

8. Impact of Caffeine on Heart Rate in Daphnia

Research Question: Does caffeine affect the heart rate of Daphnia (water fleas)?
Null Hypothesis (H0): Caffeine does not affect the heart rate of Daphnia.
Symbolic Form: H0: Heart rate with caffeine = Heart rate without caffeine

9. Influence of Soil pH on Plant Germination

Research Question: Does soil pH affect the germination rate of seeds?
Null Hypothesis (H0): Soil pH does not affect the germination rate of seeds.
Symbolic Form: H0: Germination rate at pH1 = Germination rate at pH2

10. Effect of Salinity on Aquatic Plant Growth

Research Question: Does salinity affect the growth of aquatic plants?
Null Hypothesis (H0): Salinity does not affect the growth of aquatic plants.
Symbolic Form: H0: Plant growth in saline water = Plant growth in freshwater

Null Hypothesis Examples in Business

1. effect of marketing campaign on sales.

Research Question: Does a new marketing campaign increase product sales?
Null Hypothesis (H0): The new marketing campaign does not increase product sales.
Symbolic Form: H0: ?campaign = ?no_campaign

2. Impact of Training Programs on Employee Productivity

Research Question: Do training programs improve employee productivity?
Null Hypothesis (H0): Training programs do not improve employee productivity.
Symbolic Form: H0: ?trained = ?untrained

3. Influence of Price Changes on Demand

Research Question: Do price changes affect the demand for a product?
Null Hypothesis (H0): Price changes do not affect the demand for the product.
Symbolic Form: H0: ?price_change = ?no_price_change

4. Customer Satisfaction and Service Quality

Research Question: Does improving service quality increase customer satisfaction?
Null Hypothesis (H0): Improving service quality does not increase customer satisfaction.
Symbolic Form: H0: ?improved_service = ?standard_service

5. Effect of Employee Benefits on Retention Rates

Research Question: Do enhanced employee benefits reduce turnover rates?
Null Hypothesis (H0): Enhanced employee benefits do not reduce turnover rates.
Symbolic Form: H0: ?enhanced_benefits = ?standard_benefits

6. Impact of Social Media Presence on Brand Awareness

Research Question: Does an active social media presence increase brand awareness?
Null Hypothesis (H0): An active social media presence does not increase brand awareness.
Symbolic Form: H0: ?active_social_media = ?inactive_social_media

7. Influence of Store Layout on Customer Purchases

Research Question: Does store layout affect customer purchasing behavior?
Null Hypothesis (H0): Store layout does not affect customer purchasing behavior.
Symbolic Form: H0: ?layout1 = ?layout2

8. Online Advertising and Website Traffic

Research Question: Does online advertising increase website traffic?
Null Hypothesis (H0): Online advertising does not increase website traffic.
Symbolic Form: H0: ?ads = ?no_ads

9. Effect of Product Packaging on Sales

Research Question: Does new product packaging design increase sales?
Null Hypothesis (H0): The new product packaging design does not increase sales.
Symbolic Form: H0: ?new_packaging = ?old_packaging

10. Influence of Remote Work on Employee Performance

Research Question: Does remote work affect employee performance?
Null Hypothesis (H0): Remote work does not affect employee performance.
Symbolic Form: H0: ?remote_work = ?office_work

Null Hypothesis Examples in Statistics

1. comparing means.

Research Question: Is there a difference in average test scores between two groups of students?
Null Hypothesis (H0): There is no difference in the average test scores between the two groups.

2. Proportions

Research Question: Is the proportion of defective products the same in two different production lines?
Null Hypothesis (H0): The proportion of defective products is the same in both production lines.
Symbolic Form: H0: p1 = p2

3. Regression Analysis

Research Question: Is there a relationship between years of experience and salary?
Null Hypothesis (H0): There is no relationship between years of experience and salary.
Symbolic Form: H0: ? = 0 (where ? is the regression coefficient)

4. ANOVA (Analysis of Variance)

Research Question: Are the means of three or more groups equal?
Null Hypothesis (H0): The means of all groups are equal.
Symbolic Form: H0: ?1 = ?2 = ?3 = … = ?k

5. Chi-Square Test for Independence

Research Question: Are gender and voting preference independent?
Null Hypothesis (H0): Gender and voting preference are independent.
Symbolic Form: H0: There is no association between gender and voting preference.

6. Time Series Analysis

Research Question: Does a time series exhibit a trend over time?
Null Hypothesis (H0): There is no trend in the time series data over time.
Symbolic Form: H0: The time series has no significant trend component.

7. Hypothesis Testing for Variance

Research Question: Is the variance in test scores different between two classes?
Null Hypothesis (H0): The variances in test scores are equal between the two classes.
Symbolic Form: H0: ?1² = ?2²

8. Correlation Analysis

Research Question: Is there a correlation between two variables, such as height and weight?
Null Hypothesis (H0): There is no correlation between the two variables.
Symbolic Form: H0: ? = 0 (where ? is the correlation coefficient)

9. Two-Sample t-Test

Research Question: Do two samples have the same mean?
Null Hypothesis (H0): The two samples have the same mean.

10. One-Sample t-Test

Research Question: Does the sample mean differ from a known population mean?
Null Hypothesis (H0): The sample mean is equal to the population mean.
Symbolic Form: H0: ? = ?0

Real life Examples of Null Hypothesis

1. medical studies.

Research Question: Does a new medication lower blood pressure more effectively than the current medication?
Null Hypothesis (H0): The new medication does not lower blood pressure more effectively than the current medication.
Example: A clinical trial compares blood pressure readings between patients taking the new medication and those taking the current medication.

2. Education

Research Question: Does a new teaching method improve student test scores?
Null Hypothesis (H0): The new teaching method does not improve student test scores.
Example: An educational study compares test scores of students taught using the new method versus those taught using traditional methods.

3. Business

Research Question: Does a new advertising campaign increase product sales?
Null Hypothesis (H0): The new advertising campaign does not increase product sales.
Example: A company runs the new campaign and compares sales data before and after the campaign.

4. Public Health

Research Question: Does a smoking cessation program reduce the smoking rate in a community?
Null Hypothesis (H0): The smoking cessation program does not reduce the smoking rate in the community.
Example: Public health officials analyze smoking rates before and after implementing the program.

5. Environmental Science

Research Question: Does the introduction of a specific fish species affect the biodiversity of a lake?
Null Hypothesis (H0): The introduction of the specific fish species does not affect the biodiversity of the lake.
Example: Environmental scientists monitor biodiversity levels before and after introducing the fish species.

6. Economics

Research Question: Does raising the minimum wage reduce poverty levels?
Null Hypothesis (H0): Raising the minimum wage does not reduce poverty levels.
Example: Economists compare poverty rates in regions with and without recent minimum wage increases.

7. Psychology

Research Question: Does mindfulness meditation reduce stress levels among college students?
Null Hypothesis (H0): Mindfulness meditation does not reduce stress levels among college students.
Example: A study measures stress levels before and after a mindfulness meditation program in a group of students.

8. Agriculture

Example: Farmers apply the new fertilizer to one field and a standard fertilizer to another and compare the yields.

9. Technology

Research Question: Does a new software update improve the speed of a computer program?
Null Hypothesis (H0): The new software update does not improve the speed of the computer program.
Example: Software engineers measure the program’s speed before and after applying the update.

10. Marketing

Research Question: Does personalized email marketing increase customer engagement?
Null Hypothesis (H0): Personalized email marketing does not increase customer engagement.
Example: A company sends personalized emails to one group and generic emails to another, then compares engagement rates.

More Null Hypothesis Examples & Samples in PDF

1. null hypothesis significance test example.

2. Sample Null Hypothesis Example

3. Critical Assessment of Null Hypothesis Example

4. Confidence Levels for Null Hypotheses Example

5. Interpreting Failure to Reject A Null Hypothesis Example

6. Simple Null Hypothesis Example

7. Basic Neurology Null Hypothesis Example

8. Null Research Hypothesis in DOC

Purpose of Null Hypothesis

The null hypothesis is a fundamental concept in statistics and scientific research . It serves several critical purposes in the process of hypothesis testing, guiding researchers in drawing meaningful conclusions from their data. Below are the primary purposes of the null hypothesis:

1. Baseline for Comparison

The null hypothesis provides a baseline or a default position that indicates no effect, no difference, or no relationship between variables. It is the statement that researchers aim to test against an alternative hypothesis. By starting with the assumption that there is no effect, researchers can objectively assess whether the data provide enough evidence to support the alternative hypothesis.

2. Eliminates Bias

By assuming no effect or no difference, the null hypothesis helps eliminate bias in research. Researchers approach their study without preconceived notions about the outcome, ensuring that the results are based on the data collected rather than personal beliefs or expectations.

3. Framework for Statistical Testing

The null hypothesis provides a structured framework for conducting statistical tests. It is essential for calculating p-values and test statistics, which determine whether the observed data are significantly different from what would be expected under the null hypothesis. This framework allows for a standardized approach to testing hypotheses across various fields of study.

4. Facilitates Decision Making

The null hypothesis facilitates decision-making in research by providing clear criteria for accepting or rejecting it. If the data provide sufficient evidence to reject the null hypothesis, researchers can conclude that there is a statistically significant effect or difference. This decision-making process is critical in advancing scientific knowledge and understanding.

5. Controls Type I and Type II Errors

The null hypothesis plays a crucial role in controlling Type I and Type II errors in hypothesis testing. A Type I error occurs when the null hypothesis is incorrectly rejected (a false positive), while a Type II error happens when the null hypothesis is incorrectly accepted (a false negative). By defining the null hypothesis, researchers can set significance levels (e.g., alpha level) to manage the risk of these errors.

When is the Null Hypothesis Rejected?

Rejecting the null hypothesis is a critical step in the process of hypothesis testing. The decision to reject the null hypothesis is based on statistical evidence derived from the data collected in a study. Below are the key factors that determine when the null hypothesis is rejected:

The p-value is a measure of the probability that the observed data (or something more extreme) would occur if the null hypothesis were true. The null hypothesis is rejected if the p-value is less than or equal to the predetermined significance level (?).

Significance Level (?): This is the threshold set by the researcher, commonly 0.05 (5%). If the p-value ? 0.05, the null hypothesis is rejected.
If a p-value of 0.03 is obtained and the significance level is 0.05, the null hypothesis is rejected.

2. Test Statistic

The test statistic is a standardized value calculated from sample data during a hypothesis test. It measures the degree to which the sample data differ from the null hypothesis. The decision to reject the null hypothesis depends on whether the test statistic falls within the critical region.

Critical Region: This is determined by the significance level and the distribution of the test statistic (e.g., Z-distribution, t-distribution).
In a two-tailed test with ? = 0.05, the critical region for a Z-test might be Z < -1.96 or Z > 1.96. If the test statistic is 2.10, the null hypothesis is rejected.

3. Confidence Intervals

Confidence intervals provide a range of values that are likely to contain the population parameter. If the confidence interval does not include the value specified by the null hypothesis, the null hypothesis is rejected.

If a 95% confidence interval for the mean difference between two groups is (2.5, 5.0) and the null hypothesis states that the mean difference is 0, the null hypothesis is rejected.

4. Effect Size

Effect size measures the magnitude of the difference between groups or the strength of a relationship between variables. While not a direct criterion for rejecting the null hypothesis, a substantial effect size can support the decision to reject the null hypothesis when combined with a significant p-value.

Null Hypothesis vs. Alternative Hypothesis

How to Write a Null Hypothesis

Writing a null hypothesis is a crucial step in designing a scientific study or experiment. The null hypothesis (H0) serves as a starting point for statistical testing and represents a statement of no effect or no difference. Here’s a step-by-step guide on how to write a null hypothesis:

1. Identify the Research Question

Start by clearly defining the research question you want to investigate. Understand what you are testing and what you expect to find.

Example Research Question: Does a new medication reduce blood pressure more effectively than an existing medication?

2. Determine the Variables

Identify the independent and dependent variables in your study.

Independent Variable: The variable that is manipulated or categorized (e.g., type of medication).
Dependent Variable: The variable that is measured or observed (e.g., blood pressure).

3. State the Null Hypothesis Clearly

The null hypothesis should assert that there is no effect, no difference, or no relationship between the variables. It is usually written as a statement of equality or no change.

Format: “There is no [effect/difference/relationship] in [dependent variable] between [independent variable groups].”
Example: “There is no difference in blood pressure reduction between the new medication and the existing medication.”

4. Use Proper Symbols and Notation

In formal scientific writing, use symbols and proper notation to represent the null hypothesis.

Here, ?1 represents the mean blood pressure reduction for the new medication, and ?2 represents the mean blood pressure reduction for the existing medication.

Why is the null hypothesis important?

The null hypothesis is crucial as it provides a baseline for comparison and allows researchers to test the significance of their findings.

How do you state a null hypothesis?

A null hypothesis is stated as no effect or no difference, typically in the form “There is no [effect/difference] between [groups/variables].”

What is the alternative hypothesis?

The alternative hypothesis (H1) suggests that there is an effect or difference between variables, opposing the null hypothesis.

What does it mean to reject the null hypothesis?

Rejecting the null hypothesis means the data provides sufficient evidence to support the alternative hypothesis, indicating a significant effect or difference.

What is a p-value?

A p-value measures the probability that the observed data would occur if the null hypothesis were true. Low p-values indicate strong evidence against the null hypothesis.

What is a Type I error?

A Type I error occurs when the null hypothesis is incorrectly rejected, meaning a false positive result is concluded.

What is a Type II error?

A Type II error happens when the null hypothesis is incorrectly accepted, meaning a false negative result is concluded.

How do you choose a significance level (?)?

The significance level, often set at 0.05, is chosen based on the acceptable risk of making a Type I error in the context of the study.

Can the null hypothesis be proven true?

No, the null hypothesis can only be rejected or not rejected. Failing to reject it does not prove it true, only that there is not enough evidence against it.

What is the role of sample size in hypothesis testing?

Larger sample sizes increase the test’s power, reducing the risk of Type II errors and making it easier to detect a true effect.

Text prompt

Instructive
Professional

10 Examples of Public speaking

20 Examples of Gas lighting

IMAGES

15 Null Hypothesis Examples (2024)
Null Hypothesis Examples
Hypothesis In Research
Null Hypothesis and Alternative Hypothesis
Examples of null and alternative hypotheses
Null hypothesis

COMMENTS

How to Write a Null Hypothesis (5 Examples) - Statology
Mar 10, 2021 · H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. H A (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign. We interpret the hypotheses as follows: Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.
15 Null Hypothesis Examples - Helpful Professor
Aug 26, 2023 · For example, a null hypothesis might propose a new teaching technique doesn’t enhance student performance. If data contradicts this, the technique may be beneficial. In all these areas, the null hypothesis helps minimize bias, enabling researchers to support their findings with statistically significant data.
Null and Alternative Hypotheses | Definitions & Examples
May 6, 2022 · Answering your research question with 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.”
How to Formulate a Null Hypothesis (With Examples) - ThoughtCo
May 7, 2024 · The null hypothesis is among the easiest hypothesis to test using statistical analysis, making it perhaps the most valuable hypothesis for the scientific method. By evaluating a null hypothesis in addition to another hypothesis, researchers can support their conclusions with a higher level of confidence.
Null Hypothesis | Meaning, Symbol, Formula, Test & Alternate ...
May 1, 2024 · Null hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. Learn more about Null Hypothesis, its formula, symbol and example in this article
10.1 - Setting the Hypotheses: Examples | STAT 100
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. State Null and Alternative Hypotheses. Null Hypothesis: On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg).
Null Hypothesis Examples - Science Notes and Projects
Oct 26, 2020 · The null hypothesis is the most powerful type of hypothesis in the scientific method because it’s the easiest one to test with a high confidence level using statistics. If the null hypothesis is accepted, then it’s evidence any observed differences between two experiment groups are due to random chance.
Null Hypothesis - Definition, Symbol, Formula, Types and Examples
Null Hypothesis Examples. Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way. If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”.
Null and Alternative Hypotheses | Definitions & Examples
Oct 5, 2022 · 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 ...
Null Hypothesis - 60+ Examples, Purpose, How to Write, PDFs
Jun 24, 2024 · If the confidence interval does not include the value specified by the null hypothesis, the null hypothesis is rejected. Example: If a 95% confidence interval for the mean difference between two groups is (2.5, 5.0) and the null hypothesis states that the mean difference is 0, the null hypothesis is rejected.

15 Null Hypothesis Examples

Null Hypothesis Definition

Video Explanation

Null Hypothesis Examples

Null Hypothesis vs Alternative Hypothesis

Applications of the Null Hypothesis in Research

Leave a Comment Cancel Reply

Null Hypothesis Examples

What Is the Null Hypothesis?

Examples of the Null Hypothesis

Other Types of Hypotheses

Key Takeaways

Null Hypothesis

What is Null Hypothesis?

Null Hypothesis Meaning

Mean Comparison (Two-sample t-test)

Proportion Comparison

Equality in Variance (F-test in ANOVA)

Independence (Chi-square Test of Independence):

Equality Null Hypothesis (Simple Null Hypothesis)

Non-Inferiority Null Hypothesis

Superiority Null Hypothesis

Independence Null Hypothesis

Homogeneity Null Hypothesis

Null Hypothesis Rejection

When is Null Hypothesis Rejected?

Difference Between Null Hypothesis and Alternative Hypothesis

People Also Read:

Summary - Null Hypothesis and Alternative Hypothesis

FAQs on Null Hypothesis

How to Form a Null Hypothesis?

When Do we reject the Null Hypothesis?

What is a Null Hypothesis in Research?

What Are Alternative and Null Hypotheses?

What Does it Mean to Reject the Null Hypothesis?

How to Find Null Hypothesis?

How is Null Hypothesis denoted?

What is the Purpose of the Null hypothesis in Statistical Analysis?

What happens if we Reject the Null hypothesis?

What are Test for Null Hypothesis?

Similar Reads

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

User Preferences

Keyboard Shortcuts

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

State Null and Alternative Hypotheses

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

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

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

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

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

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

Null Hypothesis Examples

What Is the Null Hypothesis?

Exact and Inexact Null Hypothesis

How to State the Null Hypothesis

Related Posts

Null Hypothesis

Null Hypothesis Definition

Null Hypothesis Symbol

Null Hypothesis Principle

Null Hypothesis Formula

Types of Null Hypothesis

Null Hypothesis Rejection

How do you Find the Null Hypothesis?

When is Null Hypothesis Rejected?

Null Hypothesis and Alternative Hypothesis

Null Hypothesis Examples

Frequently Asked Questions on Null Hypothesis

What are the benefits of hypothesis testing?

When a null hypothesis is accepted and rejected?

Why is the null hypothesis important?

How to accept or reject the null hypothesis in the chi-square test?

Register with BYJU'S & Download Free PDFs

Have a thesis expert improve your writing

Null and Alternative Hypotheses | Definitions & Examples

Table of contents

Examples of null hypotheses

Examples of alternative hypotheses