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 Null and Alternative Hypotheses  Definitions & Examples
Null & Alternative Hypotheses  Definitions, Templates & Examples
Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :
 Null hypothesis ( H 0 ): There’s no effect in the population .
 Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.
Table of contents
Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.
The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:
 The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
 The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”
The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .
You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.
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The null hypothesis is the claim that there’s no effect in the population.
If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.
Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.
Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).
You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.
Examples of null hypotheses
The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.
( )  
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 nonflossing 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 dailymeditation group ( ) is greater than or equal to the nomeditation 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 nonflossing 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 dailymeditation group ( ) is less than the nomeditation 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 testspecific template sentences. Otherwise, you can use the general template sentences.
General template sentences
The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:
Does independent variable affect dependent variable ?
 Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
 Alternative hypothesis ( H a ): Independent variable affects dependent variable.
Testspecific template sentences
Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.
( )  
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.  
Twoproportions 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 onetailed tests . Onetailed tests are appropriate for most studies.
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
 Normal distribution
 Descriptive statistics
 Measures of central tendency
 Correlation coefficient
Methodology
 Cluster sampling
 Stratified sampling
 Types of interviews
 Cohort study
 Thematic analysis
Research bias
 Implicit bias
 Cognitive bias
 Survivorship bias
 Availability heuristic
 Nonresponse bias
 Regression to the mean
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).
The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).
A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).
A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a welldesigned study , the statistical hypotheses correspond logically to the research hypothesis.
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Statistics By Jim
Making statistics intuitive
Null Hypothesis: Definition, Rejecting & Examples
By Jim Frost 6 Comments
What is a Null Hypothesis?
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.
 Null Hypothesis H 0 : No effect exists in the population.
 Alternative Hypothesis H A : The effect exists in the population.
In every study or experiment, researchers assess an effect or relationship. This effect can be the effectiveness of a new drug, building material, or other intervention that has benefits. There is a benefit or connection that the researchers hope to identify. Unfortunately, no effect may exist. In statistics, we call this lack of an effect the null hypothesis. Researchers assume that this notion of no effect is correct until they have enough evidence to suggest otherwise, similar to how a trial presumes innocence.
In this context, the analysts don’t necessarily believe the null hypothesis is correct. In fact, they typically want to reject it because that leads to more exciting finds about an effect or relationship. The new vaccine works!
You can think of it as the default theory that requires sufficiently strong evidence to reject. Like a prosecutor, researchers must collect sufficient evidence to overturn the presumption of no effect. Investigators must work hard to set up a study and a data collection system to obtain evidence that can reject the null hypothesis.
Related post : What is an Effect in Statistics?
Null Hypothesis Examples
Null hypotheses start as research questions that the investigator rephrases as a statement indicating there is no effect or relationship.
Does the vaccine prevent infections?  The vaccine does not affect the infection rate. 
Does the new additive increase product strength?  The additive does not affect mean product strength. 
Does the exercise intervention increase bone mineral density?  The intervention does not affect bone mineral density. 
As screen time increases, does test performance decrease?  There is no relationship between screen time and test performance. 
After reading these examples, you might think they’re a bit boring and pointless. However, the key is to remember that the null hypothesis defines the condition that the researchers need to discredit before suggesting an effect exists.
Let’s see how you reject the null hypothesis and get to those more exciting findings!
When to Reject the Null Hypothesis
So, you want to reject the null hypothesis, but how and when can you do that? To start, you’ll need to perform a statistical test on your data. The following is an overview of performing a study that uses a hypothesis test.
The first step is to devise a research question and the appropriate null hypothesis. After that, the investigators need to formulate an experimental design and data collection procedures that will allow them to gather data that can answer the research question. Then they collect the data. For more information about designing a scientific study that uses statistics, read my post 5 Steps for Conducting Studies with Statistics .
After data collection is complete, statistics and hypothesis testing enter the picture. Hypothesis testing takes your sample data and evaluates how consistent they are with the null hypothesis. The pvalue is a crucial part of the statistical results because it quantifies how strongly the sample data contradict the null hypothesis.
When the sample data provide sufficient evidence, you can reject the null hypothesis. In a hypothesis test, this process involves comparing the pvalue to your significance level .
Rejecting the Null Hypothesis
Reject the null hypothesis when the pvalue is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the pvalue is low, the null must go!
When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .
Failing to Reject the Null Hypothesis
Conversely, when the pvalue is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the pvalue is high, the null must fly!
Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null .
That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!
Let’s move on to learning how to write the null hypothesis for different types of effects, relationships, and tests.
Related posts : How Hypothesis Tests Work and Interpreting Pvalues
How to Write a Null Hypothesis
The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. Consequently, when you write a null hypothesis, it must make a claim about the relevant population parameter . Further, that claim usually indicates that the effect does not exist in the population. Below are typical examples of writing a null hypothesis for various parameters and hypothesis tests.
Related posts : Descriptive vs. Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics
Group Means
Ttests and ANOVA assess the differences between group means. For these tests, the null hypothesis states that there is no difference between group means in the population. In other words, the experimental conditions that define the groups do not affect the mean outcome. Mu (µ) is the population parameter for the mean, and you’ll need to include it in the statement for this type of study.
For example, an experiment compares the mean bone density changes for a new osteoporosis medication. The control group does not receive the medicine, while the treatment group does. The null states that the mean bone density changes for the control and treatment groups are equal.
 Null Hypothesis H 0 : Group means are equal in the population: µ 1 = µ 2 , or µ 1 – µ 2 = 0
 Alternative Hypothesis H A : Group means are not equal in the population: µ 1 ≠ µ 2 , or µ 1 – µ 2 ≠ 0.
Group Proportions
Proportions tests assess the differences between group proportions. For these tests, the null hypothesis states that there is no difference between group proportions. Again, the experimental conditions did not affect the proportion of events in the groups. P is the population proportion parameter that you’ll need to include.
For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the control group does not. The null states that the infection rates for the control and treatment groups are equal.
 Null Hypothesis H 0 : Group proportions are equal in the population: p 1 = p 2 .
 Alternative Hypothesis H A : Group proportions are not equal in the population: p 1 ≠ p 2 .
Correlation and Regression Coefficients
Some studies assess the relationship between two continuous variables rather than differences between groups.
In these studies, analysts often use either correlation or regression analysis . For these tests, the null states that there is no relationship between the variables. Specifically, it says that the correlation or regression coefficient is zero. As one variable increases, there is no tendency for the other variable to increase or decrease. Rho (ρ) is the population correlation parameter and beta (β) is the regression coefficient parameter.
For example, a study assesses the relationship between screen time and test performance. The null states that there is no correlation between this pair of variables. As screen time increases, test performance does not tend to increase or decrease.
 Null Hypothesis H 0 : The correlation in the population is zero: ρ = 0.
 Alternative Hypothesis H A : The correlation in the population is not zero: ρ ≠ 0.
For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis.
The preceding examples are all for twotailed hypothesis tests. To learn about onetailed tests and how to write a null hypothesis for them, read my post OneTailed vs. TwoTailed Tests .
Related post : Understanding Correlation
Neyman, J; Pearson, E. S. (January 1, 1933). On the Problem of the most Efficient Tests of Statistical Hypotheses . Philosophical Transactions of the Royal Society A . 231 (694–706): 289–337.
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Reader Interactions
January 11, 2024 at 2:57 pm
Thanks for the reply.
January 10, 2024 at 1:23 pm
Hi Jim, In your comment you state that equivalence test null and alternate hypotheses are reversed. For hypothesis tests of data fits to a probability distribution, the null hypothesis is that the probability distribution fits the data. Is this correct?
January 10, 2024 at 2:15 pm
Those two separate things, equivalence testing and normality tests. But, yes, you’re correct for both.
Hypotheses are switched for equivalence testing. You need to “work” (i.e., collect a large sample of good quality data) to be able to reject the null that the groups are different to be able to conclude they’re the same.
With typical hypothesis tests, if you have low quality data and a low sample size, you’ll fail to reject the null that they’re the same, concluding they’re equivalent. But that’s more a statement about the low quality and small sample size than anything to do with the groups being equal.
So, equivalence testing make you work to obtain a finding that the groups are the same (at least within some amount you define as a trivial difference).
For normality testing, and other distribution tests, the null states that the data follow the distribution (normal or whatever). If you reject the null, you have sufficient evidence to conclude that your sample data don’t follow the probability distribution. That’s a rare case where you hope to fail to reject the null. And it suffers from the problem I describe above where you might fail to reject the null simply because you have a small sample size. In that case, you’d conclude the data follow the probability distribution but it’s more that you don’t have enough data for the test to register the deviation. In this scenario, if you had a larger sample size, you’d reject the null and conclude it doesn’t follow that distribution.
I don’t know of any equivalence testing type approach for distribution fit tests where you’d need to work to show the data follow a distribution, although I haven’t looked for one either!
February 20, 2022 at 9:26 pm
Is a null hypothesis regularly (always) stated in the negative? “there is no” or “does not”
February 23, 2022 at 9:21 pm
Typically, the null hypothesis includes an equal sign. The null hypothesis states that the population parameter equals a particular value. That value is usually one that represents no effect. In the case of a onesided hypothesis test, the null still contains an equal sign but it’s “greater than or equal to” or “less than or equal to.” If you wanted to translate the null hypothesis from its native mathematical expression, you could use the expression “there is no effect.” But the mathematical form more specifically states what it’s testing.
It’s the alternative hypothesis that typically contains does not equal.
There are some exceptions. For example, in an equivalence test where the researchers want to show that two things are equal, the null hypothesis states that they’re not equal.
In short, the null hypothesis states the condition that the researchers hope to reject. They need to work hard to set up an experiment and data collection that’ll gather enough evidence to be able to reject the null condition.
February 15, 2022 at 9:32 am
Dear sir I always read your notes on Research methods.. Kindly tell is there any available Book on all these..wonderfull Urgent
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Home » What is a Hypothesis – Types, Examples and Writing Guide
What is a Hypothesis – Types, Examples and Writing Guide
Table of Contents
Definition:
Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.
Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.
Types of Hypothesis
Types of Hypothesis are as follows:
Research Hypothesis
A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.
Null Hypothesis
The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.
Alternative Hypothesis
An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.
Directional Hypothesis
A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.
Nondirectional Hypothesis
A nondirectional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.
Statistical Hypothesis
A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.
Composite Hypothesis
A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several subhypotheses, each of which represents a different possible outcome.
Empirical Hypothesis
An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.
Simple Hypothesis
A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.
Complex Hypothesis
A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.
Applications of Hypothesis
Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:
 Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
 Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
 Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
 Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
 Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
 Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.
How to write a Hypothesis
Here are the steps to follow when writing a hypothesis:
Identify the Research Question
The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.
Conduct a Literature Review
Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.
Determine the Variables
The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.
Formulate the Hypothesis
Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.
Write the Null Hypothesis
The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.
Refine the Hypothesis
After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.
Examples of Hypothesis
Here are a few examples of hypotheses in different fields:
 Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
 Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
 Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
 Education : “Implementing a new teaching method will result in higher student achievement scores.”
 Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
 Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
 Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”
Purpose of Hypothesis
The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.
The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.
In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.
When to use Hypothesis
Here are some common situations in which hypotheses are used:
 In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
 In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
 I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.
Characteristics of Hypothesis
Here are some common characteristics of a hypothesis:
 Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
 Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
 Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
 Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
 Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and welldesigned.
 Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
 Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.
Advantages of Hypothesis
Hypotheses have several advantages in scientific research and experimentation:
 Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
 Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
 Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
 Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
 Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
 Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.
Limitations of Hypothesis
Some Limitations of the Hypothesis are as follows:
 Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
 May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
 May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
 Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
 Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
 May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.
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AP®︎/College Statistics
Course: ap®︎/college statistics > unit 10.
 Idea behind hypothesis testing
Examples of null and alternative hypotheses
 Writing null and alternative hypotheses
 Pvalues and significance tests
 Comparing Pvalues to different significance levels
 Estimating a Pvalue from a simulation
 Estimating Pvalues from simulations
 Using Pvalues to make conclusions
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Video transcript
Null Hypothesis Definition and Examples
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In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or nodifference hypothesis.
The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a nonrandom factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .
How to State a Null Hypothesis
There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.
For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.
The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."
This can be written mathematically as: H 1 : μ > 6
In this example, μ is the average.
Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:
H 0 : μ ≤ 6
The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:
H 0 : μ = 6
 Null Hypothesis Examples
"Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.
Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.
Why Test a Null Hypothesis?
You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.
For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.
 Difference Between Independent and Dependent Variables
 Examples of Independent and Dependent Variables
 What Are Examples of a Hypothesis?
 What Is a Hypothesis? (Science)
 What 'Fail to Reject' Means in a Hypothesis Test
 What Are the Elements of a Good Hypothesis?
 Scientific Hypothesis Examples
 Null Hypothesis and Alternative Hypothesis
 What Is a Control Group?
 Understanding Simple vs Controlled Experiments
 Six Steps of the Scientific Method
 Scientific Method Vocabulary Terms
 Definition of a Hypothesis
 How to Conduct a Hypothesis Test
 Type I and Type II Errors in Statistics
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9.1: Null and Alternative Hypotheses
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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.
\(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
\(H_a\): The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\). This is usually what the researcher is trying to prove.
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis.
equal (=)  not equal \((\neq)\) greater than (>) less than (<) 
greater than or equal to \((\geq)\)  less than (<) 
less than or equal to \((\geq)\)  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 coauthors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
Example \(\PageIndex{1}\)
 \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
 \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)
Exercise \(\PageIndex{1}\)
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
 \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
 \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)
Example \(\PageIndex{2}\)
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
 \(H_{0}: \mu = 2.0\)
 \(H_{a}: \mu \neq 2.0\)
Exercise \(\PageIndex{2}\)
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.
 \(H_{0}: \mu \_ 66\)
 \(H_{a}: \mu \_ 66\)
 \(H_{0}: \mu = 66\)
 \(H_{a}: \mu \neq 66\)
Example \(\PageIndex{3}\)
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
 \(H_{0}: \mu \geq 5\)
 \(H_{a}: \mu < 5\)
Exercise \(\PageIndex{3}\)
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.
 \(H_{0}: \mu \_ 45\)
 \(H_{a}: \mu \_ 45\)
 \(H_{0}: \mu \geq 45\)
 \(H_{a}: \mu < 45\)
Example \(\PageIndex{4}\)
In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
 \(H_{0}: p \leq 0.066\)
 \(H_{a}: p > 0.066\)
Exercise \(\PageIndex{4}\)
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.
 \(H_{0}: p \_ 0.40\)
 \(H_{a}: p \_ 0.40\)
 \(H_{0}: p = 0.40\)
 \(H_{a}: p > 0.40\)
COLLABORATIVE EXERCISE
Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.
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 \((=, \leq \text{or} \geq)\)
 Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
 If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
 Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of nonabsolute certainties.
Formula Review
\(H_{0}\) and \(H_{a}\) are contradictory.
equal \((=)\)  greater than or equal to \((\geq)\)  less than or equal to \((\leq)\)  
has:  not equal \((\neq)\) greater than \((>)\) less than \((<)\)  less than \((<)\)  greater than \((>)\) 
 If \(\alpha \leq p\)value, then do not reject \(H_{0}\).
 If\(\alpha > p\)value, then reject \(H_{0}\).
\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)value is calculated from the data.References
Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .
 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 Hnull or Hzero or Hnought. At the same time, the alternative hypothesis expresses the observations determined by the nonrandom 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 Pvalue approach. If the Pvalue 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 Pvalue 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.

 
1  The null hypothesis is a statement. There exists no relation between two variables  Alternative hypothesis a statement, there exists some relationship between two measured phenomenon 
2  Denoted by H  Denoted by H 
3  The observations of this hypothesis are the result of chance  The observations of this hypothesis are the result of real effect 
4  The mathematical formulation of the null hypothesis is an equal sign  The mathematical formulation alternative hypothesis is an inequality sign such as greater than, less than, etc. 
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 grownups 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 grownups?
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 Pvalue is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the Pvalue 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 chisquare test?
If the result of the chisquare 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.
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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 (Twosample ttest)
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 (Ftest in ANOVA)
H 0 : σ 1 = σ 2
This states that there’s no significant difference in variances between groups or populations.
Independence (Chisquare 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.
NonInferiority 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 chisquare 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 postimplementation 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 [Tex]\alpha [/Tex] ) 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.
Criteria  Null Hypothesis  Alternative Hypothesis 

Definition  Assumes no effect or difference  Asserts a specific effect or difference 
Symbol  H  H (or Ha) 
Formulation  States equality or absence of parameter  States a specific value or relationship 
Testing Outcome  Rejected if evidence of a significant effect  Accepted if evidence supports the hypothesis 
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.
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Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.
Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a ttest, if the calculated tstatistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.
Example 2: A company asserts that the error rate in its production process is less than 1%.
Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a ztest, if the calculated zstatistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.
Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?
Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?
Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?
Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?
Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?
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 pvalue (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 ttests or chisquare tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.
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Hypothesis  Meaning in Bengali
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9.1 Null and Alternative Hypotheses
The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.
H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.
Mathematical Symbols Used in H 0 and H a :
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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Hypothesis Meaning In Bengali
সাধারণ উদাহরণ এবং সংজ্ঞা সহ hypothesis এর আসল অর্থ জানুন।., definitions of hypothesis.
1 . একটি অনুমান বা ব্যাখ্যা সীমিত প্রমাণের ভিত্তিতে আরও তদন্তের জন্য একটি সূচনা বিন্দু হিসাবে দেওয়া হয়েছে।
1 . a supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation.
সমার্থক শব্দ
Examples of hypothesis :.
1 . প্যানস্পারমিয়া হাইপোথিসিস বিকল্পভাবে পরামর্শ দেয় যে উল্কাপিণ্ড, গ্রহাণু এবং অন্যান্য ছোট সৌরজগতের সংস্থাগুলির দ্বারা প্রাথমিক পৃথিবীতে মাইক্রোস্কোপিক জীবন বিতরণ করা হয়েছিল এবং মহাবিশ্ব জুড়ে জীবন থাকতে পারে।
1 . the panspermia hypothesis alternatively suggests that microscopic life was distributed to the early earth by meteoroids, asteroids and other small solar system bodies and that life may exist throughout the universe.
2 . নাল হাইপোথিসিস টেস্টিং গুরুত্বপূর্ণ।
2 . Null hypothesis testing is important.
3 . ধারাবাহিক অনুমান।
3 . the continuum hypothesis .
4 . একটি যাচাইযোগ্য অনুমান
4 . an unverifiable hypothesis
5 . প্রতিটি হাইপোথিসিস, যা অন্টোলজিকাল নীতিগুলির একটির বিপরীতে, ভুল।
5 . Each hypothesis , which contradicts one of the ontological principles, is wrong.
6 . প্যানস্পারমিয়া হাইপোথিসিস থেকে জানা যায় যে পৃথিবীর প্রথম দিকে মহাকাশের ধূলিকণা, উল্কাপিণ্ড, গ্রহাণু এবং অন্যান্য ছোট সৌরজগতের দ্বারা মাইক্রোস্কোপিক জীবন বিতরণ করা হয়েছিল এবং মহাবিশ্ব জুড়ে জীবন থাকতে পারে।
6 . the panspermia hypothesis suggests that microscopic life was distributed to the early earth by space dust, meteoroids, asteroids and other small solar system bodies and that life may exist throughout the universe.
7 . একটি পরীক্ষাযোগ্য অনুমান
7 . a testable hypothesis
8 . ফ্যান্টম টাইম হাইপোথিসিস।
8 . phantom time hypothesis .
9 . এই অনুমান পরীক্ষা করার জন্য, ড.
9 . to test this hypothesis , dr.
10 . আমি আমার অনুমান সঠিক ছিল.
10 . i was correct in my hypothesis .
11 . দ্য হ্যাপিনেস হাইপোথিসিস" হাইড্ট।
11 . the happiness hypothesis " haidt.
12 . এই ঢাল একটি নতুন হাইপোথিসিস উত্থাপন.
12 . this slope raises a new hypothesis .
13 . হাইপোথিসিস বি: ইতিহাসের একটি অর্থ আছে।
13 . Hypothesis B: history has a meaning.
14 . এটি sapirwhorf হাইপোথিসিসের সাথে মিলে যায়।
14 . this corresponds to the sapirwhorf hypothesis .
15 . আমি একটি অনুমান আছে যে সঠিক হতে পারে বা নাও হতে পারে.
15 . i have a hypothesis that may or may not be right.
16 . অনুমানটি কেবল অপ্রমাণযোগ্য নয়, তবে মিথ্যা
16 . the hypothesis is not merely unprovable, but false
17 . তিনি সবার কাছে শপথ করেছিলেন যে হাইপোথিসিস কাজ করবে।
17 . She swore to everyone that the hypothesis would work.
18 . … অথবা হাইপোথিসিস প্রত্যাখ্যানের জন্য একটি "অনুরোধ"?
18 . … or a “Requiem” for the rejection of the hypothesis ?
19 . আপনি কিভাবে একটি শূন্য অনুমান প্রত্যাখ্যান করতে ANOVA ব্যবহার করতে পারেন?
19 . How can you use the ANOVA to reject a null hypothesis ?
20 . খুব ভালো; এই অন্য অনুমান আপনি তাহলে কি বলেন?
20 . Very good; what say you then to this other hypothesis ?
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Statistics Made Easy
How to Write a Null Hypothesis (5 Examples)
A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:
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.
Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.
For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.
To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:
H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)
H A : μ > 20 (the true mean height of plants is greater than 20 inches)
If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.
Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.
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:
H 0 : μ = 300 (the true mean weight is equal to 300 pounds)
H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)
Example 2: Height of Males
It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.
H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)
H A : μ > 68 (the true mean height is greater than 68 inches)
Example 3: Graduation Rates
A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.
H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)
H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)
Example 4: Burger Weights
A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.
H 0 : μ = 7 (the true mean weight is equal to 7 ounces)
H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)
Example 5: Citizen Support
A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.
H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)
H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)
Additional Resources
Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of PValues and Statistical Significance
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2 Replies to “How to Write a Null Hypothesis (5 Examples)”
you are amazing, thank you so much
Say I am a botanist hypothesizing the average height of daisies is 20 inches, or not? Does T = (ave – 20 inches) / √ variance / (80 / 4)? … This assumes 40 real measures + 40 fake = 80 n, but that seems questionable. Please advise.
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What is The Null Hypothesis & When Do You Reject The Null Hypothesis
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On This Page:
A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.
The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).
The null hypothesis is the statement that a researcher or an investigator wants to disprove.
Testing the null hypothesis can tell you whether your results are due to the effects of manipulating the dependent variable or due to random chance.
How to Write a Null Hypothesis
Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.
It is a default position that your research aims to challenge or confirm.
For example, if studying the impact of exercise on weight loss, your null hypothesis might be:
There is no significant difference in weight loss between individuals who exercise daily and those who do not.
Examples of Null Hypotheses
Research Question  Null Hypothesis 

Do teenagers use cell phones more than adults?  Teenagers and adults use cell phones the same amount. 
Do tomato plants exhibit a higher rate of growth when planted in compost rather than in soil?  Tomato plants show no difference in growth rates when planted in compost rather than soil. 
Does daily meditation decrease the incidence of depression?  Daily meditation does not decrease the incidence of depression. 
Does daily exercise increase test performance?  There is no relationship between daily exercise time and test performance. 
Does the new vaccine prevent infections?  The vaccine does not affect the infection rate. 
Does flossing your teeth affect the number of cavities?  Flossing your teeth has no effect on the number of cavities. 
When Do We Reject The Null Hypothesis?
We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the pvalue (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.
If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected.
Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).
If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables.
You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A pvalue is one statistical measurement used to validate a hypothesis against observed data.
Calculating the pvalue is a critical part of nullhypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.
The level of statistical significance is often expressed as a p value between 0 and 1. The smaller the pvalue, the stronger the evidence that you should reject the null hypothesis.
Usually, a researcher uses a confidence level of 95% or 99% (pvalue of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.
When your pvalue is less than or equal to your significance level, you reject the null hypothesis.
In other words, smaller pvalues are taken as stronger evidence against the null hypothesis. Conversely, when the pvalue is greater than your significance level, you fail to reject the null hypothesis.
In this case, the sample data provides insufficient data to conclude that the effect exists in the population.
Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.
When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.
Why Do We Never Accept The Null Hypothesis?
The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.
A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist.
It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null.
One can either reject the null hypothesis, or fail to reject it, but can never accept it.
Why Do We Use The Null Hypothesis?
We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.
The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).
A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.
Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.
Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.
It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter.
Purpose of a Null Hypothesis
 The primary purpose of the null hypothesis is to disprove an assumption.
 Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
 A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.
Do you always need both a Null Hypothesis and an Alternative Hypothesis?
The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true.
While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.
The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study.
What is the difference between a null hypothesis and an alternative hypothesis?
The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.
It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.
What are some problems with the null hypothesis?
One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.
Why can a null hypothesis not be accepted?
We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.
We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.
Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.
If the pvalue is greater than the significance level, then you fail to reject the null hypothesis.
Is a null hypothesis directional or nondirectional?
A hypothesis test can either contain an alternative directional hypothesis or a nondirectional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.
A nondirectional hypothesis contains the not equal sign (“≠”). However, a null hypothesis is neither directional nor nondirectional.
A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.
The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.
Gill, J. (1999). The insignificance of null hypothesis significance testing. Political research quarterly , 52 (3), 647674.
Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method. American Psychologist , 56 (1), 16.
Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to nullhypothesis significance testing. Behavior research methods , 43 , 679690.
Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy. Psychological methods , 5 (2), 241.
Rozeboom, W. W. (1960). The fallacy of the nullhypothesis significance test. Psychological bulletin , 57 (5), 416.
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What is a scientific hypothesis?
It's the initial building block in the scientific method.
Hypothesis basics
What makes a hypothesis testable.
 Types of hypotheses
 Hypothesis versus theory
Additional resources
Bibliography.
A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method . Many describe it as an "educated guess" based on prior knowledge and observation. While this is true, a hypothesis is more informed than a guess. While an "educated guess" suggests a random prediction based on a person's expertise, developing a hypothesis requires active observation and background research.
The basic idea of a hypothesis is that there is no predetermined outcome. For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation. This concept, called falsifiability and testability, was advanced in the mid20th century by AustrianBritish philosopher Karl Popper in his famous book "The Logic of Scientific Discovery" (Routledge, 1959).
A key function of a hypothesis is to derive predictions about the results of future experiments and then perform those experiments to see whether they support the predictions.
A hypothesis is usually written in the form of an ifthen statement, which gives a possibility (if) and explains what may happen because of the possibility (then). The statement could also include "may," according to California State University, Bakersfield .
Here are some examples of hypothesis statements:
 If garlic repels fleas, then a dog that is given garlic every day will not get fleas.
 If sugar causes cavities, then people who eat a lot of candy may be more prone to cavities.
 If ultraviolet light can damage the eyes, then maybe this light can cause blindness.
A useful hypothesis should be testable and falsifiable. That means that it should be possible to prove it wrong. A theory that can't be proved wrong is nonscientific, according to Karl Popper's 1963 book " Conjectures and Refutations ."
An example of an untestable statement is, "Dogs are better than cats." That's because the definition of "better" is vague and subjective. However, an untestable statement can be reworded to make it testable. For example, the previous statement could be changed to this: "Owning a dog is associated with higher levels of physical fitness than owning a cat." With this statement, the researcher can take measures of physical fitness from dog and cat owners and compare the two.
Types of scientific hypotheses
In an experiment, researchers generally state their hypotheses in two ways. The null hypothesis predicts that there will be no relationship between the variables tested, or no difference between the experimental groups. The alternative hypothesis predicts the opposite: that there will be a difference between the experimental groups. This is usually the hypothesis scientists are most interested in, according to the University of Miami .
For example, a null hypothesis might state, "There will be no difference in the rate of muscle growth between people who take a protein supplement and people who don't." The alternative hypothesis would state, "There will be a difference in the rate of muscle growth between people who take a protein supplement and people who don't."
If the results of the experiment show a relationship between the variables, then the null hypothesis has been rejected in favor of the alternative hypothesis, according to the book " Research Methods in Psychology " (BCcampus, 2015).
There are other ways to describe an alternative hypothesis. The alternative hypothesis above does not specify a direction of the effect, only that there will be a difference between the two groups. That type of prediction is called a twotailed hypothesis. If a hypothesis specifies a certain direction — for example, that people who take a protein supplement will gain more muscle than people who don't — it is called a onetailed hypothesis, according to William M. K. Trochim , a professor of Policy Analysis and Management at Cornell University.
Sometimes, errors take place during an experiment. These errors can happen in one of two ways. A type I error is when the null hypothesis is rejected when it is true. This is also known as a false positive. A type II error occurs when the null hypothesis is not rejected when it is false. This is also known as a false negative, according to the University of California, Berkeley .
A hypothesis can be rejected or modified, but it can never be proved correct 100% of the time. For example, a scientist can form a hypothesis stating that if a certain type of tomato has a gene for red pigment, that type of tomato will be red. During research, the scientist then finds that each tomato of this type is red. Though the findings confirm the hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, the hypothesis is true, but it may not be true 100% of the time.
Scientific theory vs. scientific hypothesis
The best hypotheses are simple. They deal with a relatively narrow set of phenomena. But theories are broader; they generally combine multiple hypotheses into a general explanation for a wide range of phenomena, according to the University of California, Berkeley . For example, a hypothesis might state, "If animals adapt to suit their environments, then birds that live on islands with lots of seeds to eat will have differently shaped beaks than birds that live on islands with lots of insects to eat." After testing many hypotheses like these, Charles Darwin formulated an overarching theory: the theory of evolution by natural selection.
"Theories are the ways that we make sense of what we observe in the natural world," Tanner said. "Theories are structures of ideas that explain and interpret facts."
 Read more about writing a hypothesis, from the American Medical Writers Association.
 Find out why a hypothesis isn't always necessary in science, from The American Biology Teacher.
 Learn about null and alternative hypotheses, from Prof. Essa on YouTube .
Encyclopedia Britannica. Scientific Hypothesis. Jan. 13, 2022. https://www.britannica.com/science/scientifichypothesis
Karl Popper, "The Logic of Scientific Discovery," Routledge, 1959.
California State University, Bakersfield, "Formatting a testable hypothesis." https://www.csub.edu/~ddodenhoff/Bio100/Bio100sp04/formattingahypothesis.htm
Karl Popper, "Conjectures and Refutations," Routledge, 1963.
Price, P., Jhangiani, R., & Chiang, I., "Research Methods of Psychology — 2nd Canadian Edition," BCcampus, 2015.
University of Miami, "The Scientific Method" http://www.bio.miami.edu/dana/161/evolution/161app1_scimethod.pdf
William M.K. Trochim, "Research Methods Knowledge Base," https://conjointly.com/kb/hypothesesexplained/
University of California, Berkeley, "Multiple Hypothesis Testing and False Discovery Rate" https://www.stat.berkeley.edu/~hhuang/STAT141/LectureFDR.pdf
University of California, Berkeley, "Science at multiple levels" https://undsci.berkeley.edu/article/0_0_0/howscienceworks_19
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শূন্যঅনুমান. নাস্তি কল্পনা (ইংরেজি: null hypothesis) হল, যে পরিসংখ্যানিক ...
Z Test in Bengali: How to test significance of two means  Null Hypothesis Testing  Z Test problemsYou may also like the videos :Psychology:https://www.yout...
What is Hypothesis in Bengali: Meaning  Characteristics  Types of Hypothesis with examplesIn this video I discussed about meaning, characteristics and typ...
নাস্তি কল্পনা(Null Hypothesis),জেড টেস্ট,(Ztest), null hypothesis and alternative hypothesis bangla→ ...
Basic definitions. The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise.. The statement being tested in a test of statistical significance is called the null hypothesis. . The test of significance is designed ...
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 ( H0) answers "No, there's no effect in the population.". The alternative hypothesis ( Ha) answers "Yes, there is an effect in the ...
Translation of "null hypothesis" into Bangla . নাস্তি কল্পনা is the translation of "null hypothesis" into Bangla. Sample translated sentence: Hence, the null hypothesis at the 5% level is not rejected. ↔ অর্থাৎ পূর্ণ সংখ্যার সেটে ৫ এর কোন বিপরীতক নেই।
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant.
A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence. Write the Null Hypothesis. The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing.
HYPOTHESIS translate: অনুমান, অনুমেয় প্রস্তাব. Learn more in the Cambridge EnglishBengali Dictionary.
It is the opposite of your research hypothesis. The alternative hypothesisthat is, the research hypothesisis 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.
Examples. A research hypothesis, in its plural form "hypotheses," is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.
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.
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Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
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 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 ...
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. It serves as a baseline assumption, positing no observed change or effect occurring.
Hypothesis meaning in Bengali  আগে থেকেই যা সত্য বলে মেনে নেওয়া হয়েছে;  English  Bangla & English (E2B) Online Dictionary. ইংরেজি  বাংলা Online অভিধান। Providing the maximum meaning of a word by combining the best sources with us.
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.
Hypothesis meaning in Bengali  Learn actual meaning of Hypothesis with simple examples & definitions. Also you will learn Antonyms , synonyms & best example sentences. This dictionary also provide you 10 languages so you can find meaning of Hypothesis in Hindi, Tamil , Telugu , Bengali , Kannada , Marathi , Malayalam , Gujarati , Punjabi , Urdu.
Previous Years NTA NET Questions: Hypothesis  Null Hypothesis  Research  Paper 1  EducationWhat is Hypothesis in Bengali: Meaning  Characteristics  Ty...
A pvalue, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e., that the null hypothesis is true). The level of statistical significance is often expressed as a pvalue between 0 and 1. The smaller the p value, the less likely the results occurred by random chance, and the ...
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. HA (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign.
A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis. Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.
A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method. Many describe it as an "educated guess ...