greater than (>) less than (<)
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.
H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30
H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.
H 0 : The drug reduces cholesterol by 25%. p = 0.25
H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:
H 0 : μ = 2.0
H a : μ ≠ 2.0
We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
H 0 : μ ≥ 5
H a : μ < 5
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
H 0 : p ≤ 0.066
H a : p > 0.066
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
H 0 and H a are contradictory.
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10.1 - setting the hypotheses: examples.
A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.
About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.
A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.
Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.
Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.
This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.
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Figuring out exactly what the null hypothesis and the alternative hypotheses are is not a walk in the park. Hypothesis testing is based on the knowledge that you can acquire by going over what we have previously covered about statistics in our blog.
So, if you don’t want to have a hard time keeping up, make sure you have read all the tutorials about confidence intervals , distributions , z-tables and t-tables .
We've also made a video on null hypothesis vs alternative hypothesis - you can watch it below or just scroll down if you prefer reading.
Confidence intervals provide us with an estimation of where the parameters are located. You can obtain them with our confidence interval calculator and learn more about them in the related article.
However, when we are making a decision, we need a yes or no answer. The correct approach, in this case, is to use a test .
Here we will start learning about one of the fundamental tasks in statistics - hypothesis testing !
First off, let’s talk about data-driven decision-making. It consists of the following steps:
Let’s start from the beginning.
Though there are many ways to define it, the most intuitive must be:
“A hypothesis is an idea that can be tested.”
This is not the formal definition, but it explains the point very well.
So, if we say that apples in New York are expensive, this is an idea or a statement. However, it is not testable, until we have something to compare it with.
For instance, if we define expensive as: any price higher than $1.75 dollars per pound, then it immediately becomes a hypothesis .
An example may be: would the USA do better or worse under a Clinton administration, compared to a Trump administration? Statistically speaking, this is an idea , but there is no data to test it. Therefore, it cannot be a hypothesis of a statistical test.
Actually, it is more likely to be a topic of another discipline.
Conversely, in statistics, we may compare different US presidencies that have already been completed. For example, the Obama administration and the Bush administration, as we have data on both.
Alright, let’s get out of politics and get into hypotheses . Here’s a simple topic that CAN be tested.
According to Glassdoor (the popular salary information website), the mean data scientist salary in the US is 113,000 dollars.
So, we want to test if their estimate is correct.
There are two hypotheses that are made: the null hypothesis , denoted H 0 , and the alternative hypothesis , denoted H 1 or H A .
The null hypothesis is the one to be tested and the alternative is everything else. In our example:
The null hypothesis would be: The mean data scientist salary is 113,000 dollars.
While the alternative : The mean data scientist salary is not 113,000 dollars.
Author's note: If you're interested in a data scientist career, check out our articles Data Scientist Career Path , 5 Business Basics for Data Scientists , Data Science Interview Questions , and 15 Data Science Consulting Companies Hiring Now .
You can also form one-sided or one-tailed tests.
Say your friend, Paul, told you that he thinks data scientists earn more than 125,000 dollars per year. You doubt him, so you design a test to see who’s right.
The null hypothesis of this test would be: The mean data scientist salary is more than 125,000 dollars.
The alternative will cover everything else, thus: The mean data scientist salary is less than or equal to 125,000 dollars.
Important: The outcomes of tests refer to the population parameter rather than the sample statistic! So, the result that we get is for the population.
Important: Another crucial consideration is that, generally, the researcher is trying to reject the null hypothesis . Think about the null hypothesis as the status quo and the alternative as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging.
Let’s go over it once more. In statistics, the null hypothesis is the statement we are trying to reject. Therefore, the null hypothesis is the present state of affairs, while the alternative is our personal opinion.
Right now, you may be feeling a little puzzled. This is normal because this whole concept is counter-intuitive at the beginning. However, there is an extremely easy way to continue your journey of exploring it. By diving into the linked tutorial, you will find out why hypothesis testing actually works.
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Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.
There are 5 main steps in hypothesis testing:
Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.
Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.
After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.
The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.
For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.
There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).
If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.
Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.
Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .
Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.
In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.
In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).
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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .
In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.
In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.
However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.
If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”
These are superficial differences; you can see that they mean the same thing.
You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.
If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .
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.
Methodology
Research bias
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.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
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.
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04.28.2023 • 5 min read
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Learn about a null versus alternative hypothesis and what they show with examples for each. Also go over the main differences and similarities between them.
In This Article
What is an alternative hypothesis, outcomes of a hypothesis test.
Main Differences Between Null & Alternative Hypothesis
Similarities Between Null & Alternative Hypothesis
Hypothesis Testing & Errors
In statistics, you’ll draw insights or “inferences” about population parameters using data from a sample. This process is called inferential statistics.
To make statistical inferences, you need to determine if you have enough evidence to support a certain hypothesis about the population. This is where null and alternative hypotheses come into play!
In this article, we’ll explain the differences between these two types of hypotheses, and we’ll explain the role they play in hypothesis testing.
Imagine you want to know what percent of Americans are vegetarians. You find a Gallup poll claiming 5% of the population was vegetarian in 2018, but your intuition tells you vegetarianism is on the rise and that far more than 5% of Americans are vegetarian today.
To investigate further, you collect your own sample data by surveying 1,000 randomly selected Americans. You’ll use this random sample to determine whether it’s likely the true population proportion of vegetarians is, in fact, 5% (as the Gallup data suggests) or whether it could be the case that the percentage of vegetarians is now higher.
Notice that your investigation involves two rival hypotheses about the population. One hypothesis is that the proportion of vegetarians is 5%. The other hypothesis is that the proportion of vegetarians is greater than 5%. In statistics, we would call the first hypothesis the null hypothesis, and the second hypothesis the alternative hypothesis. The null hypothesis ( H 0 H_0 H 0 ) represents the status quo or what is assumed to be true about the population at the start of your investigation.
Null Hypothesis
In hypothesis testing, the null hypothesis ( H 0 H_0 H 0 ) is the default hypothesis.
It's what the status quo assumes to be true about the population.
The alternative hypothesis ( H a H_a H a or H 1 H_1 H 1 ) is the hypothesis that stands contrary to the null hypothesis. The alternative hypothesis represents the research hypothesis—what you as the statistician are trying to prove with your data .
In medical studies, where scientists are trying to demonstrate whether a treatment has a significant effect on patient outcomes, the alternative hypothesis represents the hypothesis that the treatment does have an effect, while the null hypothesis represents the assumption that the treatment has no effect.
Alternative Hypothesis
The alternative hypothesis ( H a H_a H a or H 1 H_1 H 1 ) is the hypothesis being proposed in opposition to the null hypothesis.
In a hypothesis test, the null and alternative hypotheses must be mutually exclusive statements, meaning both hypotheses cannot be true at the same time. For example, if the null hypothesis includes an equal sign, the alternative hypothesis must state that the values being mentioned are “not equal” in some way.
Your hypotheses will also depend on the formulation of your test—are you running a one-sample T-test, a two-sample T-test, F-test for ANOVA , or a Chi-squared test? It also matters whether you are conducting a directional one-tailed test or a nondirectional two-tailed test.
Null Hypothesis: The population mean is equal to some number, x. 𝝁 = x
Alternative Hypothesis: The population mean is not equal to x. 𝝁 ≠ x
Null Hypothesis: The population mean is less than or equal to some number, x. 𝝁 ≤ x Alternative Hypothesis: The population mean is greater than x. 𝝁 > x
Null Hypothesis: The population mean is greater than or equal to some number, x. 𝝁 ≥ x
Alternative Hypothesis: The population mean is less than x. 𝝁 < x
By the end of a hypothesis test, you will have reached one of two conclusions.
You will run into either 2 outcomes:
Fail to reject the null hypothesis on the grounds that there's insufficient evidence to move away from the null hypothesis
Reject the null hypothesis in favor of the alternative.
If you’re confused about the outcomes of a hypothesis test, a good analogy is a jury trial. In a jury trial, the defendant is innocent until proven guilty. To reach a verdict of guilt, the jury must find strong evidence (beyond a reasonable doubt) that the defendant committed the crime.
This is analogous to a statistician who must assume the null hypothesis is true unless they can uncover strong evidence ( a p-value less than or equal to the significance level) in support of the alternative hypothesis.
Notice also, that a jury never concludes a defendant is innocent—only that the defendant is guilty or not guilty. This is similar to how we never conclude that the null hypothesis is true. In a hypothesis test, we never conclude that the null hypothesis is true. We can only “reject” the null hypothesis or “fail to reject” it.
In this video, let’s look at the jury example again, the reasoning behind hypothesis testing, and how to form a test. It starts by stating your null and alternative hypotheses.
Here is a summary of the key differences between the null and the alternative hypothesis test.
The null hypothesis represents the status quo; the alternative hypothesis represents an alternative statement about the population.
The null and the alternative are mutually exclusive statements, meaning both statements cannot be true at the same time.
In a medical study, the null hypothesis represents the assumption that a treatment has no statistically significant effect on the outcome being studied. The alternative hypothesis represents the belief that the treatment does have an effect.
The null hypothesis is denoted by H_0 ; the alternative hypothesis is denoted by H_a H_1
You “fail to reject” the null hypothesis when the p-value is larger than the significance level. You “reject” the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to your test’s significance level.
The similarities between the null and alternative hypotheses are as follows.
Both the null and the alternative are statements about the same underlying data.
Both statements provide a possible answer to a statistician’s research question.
The same hypothesis test will provide evidence for or against the null and alternative hypotheses.
Always remember that statistical inference provides you with inferences based on probability rather than hard truths. Anytime you conduct a hypothesis test, there is a chance that you’ll reach the wrong conclusion about your data.
In statistics, we categorize these wrong conclusions into two types of errors:
Type I Errors
Type II Errors
A Type I error occurs when you reject the null hypothesis when, in fact, the null hypothesis is true. This is sometimes called a false positive and is analogous to a jury that falsely convicts an innocent defendant. The probability of making this type of error is represented by alpha, ɑ.
A Type II error occurs when you fail to reject the null hypothesis when, in fact, the null hypothesis is false. This is sometimes called a false negative and is analogous to a jury that reaches a verdict of “not guilty,” when, in fact, the defendant has committed the crime. The probability of making this type of error is represented by beta, ꞵ.
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Learning objectives.
A hypothesis test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints and only one of these hypotheses is true. The hypothesis test determines which hypothesis is most likely true.
Because the null and alternative hypotheses are contradictory, we must examine evidence to decide if we have enough evidence to reject the null hypothesis or not reject the null hypothesis. The evidence is in the form of sample data. After we have determined which hypothesis the sample data supports, we make a decision. There are two options for a decision . They are “ reject [latex]H_0[/latex] ” if the sample information favors the alternative hypothesis or “ do not reject [latex]H_0[/latex] ” if the sample information is insufficient to reject the null hypothesis.
Watch this video: Simple hypothesis testing | Probability and Statistics | Khan Academy by Khan Academy [6:24]
A candidate in a local election claims that 30% of registered voters voted in a recent election. Information provided by the returning office suggests that the percentage is higher than the 30% claimed.
The parameter under study is the proportion of registered voters, so we use [latex]p[/latex] in the statements of the hypotheses. The hypotheses are
[latex]\begin{eqnarray*} \\ H_0: & & p=30\% \\ \\ H_a: & & p \gt 30\% \\ \\ \end{eqnarray*}[/latex]
A medical researcher believes that a new medicine reduces cholesterol by 25%. A medical trial suggests that the percent reduction is different than claimed. State the null and alternative hypotheses.
[latex]\begin{eqnarray*} H_0: & & p=25\% \\ \\ H_a: & & p \neq 25\% \end{eqnarray*}[/latex]
We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). State the null and alternative hypotheses.
[latex]\begin{eqnarray*} H_0: & & \mu=2 \mbox{ points} \\ \\ H_a: & & \mu \neq 2 \mbox{ points} \end{eqnarray*}[/latex]
We want to test whether or not the mean height of eighth graders is 66 inches. State the null and alternative hypotheses.
[latex]\begin{eqnarray*} H_0: & & \mu=66 \mbox{ inches} \\ \\ H_a: & & \mu \neq 66 \mbox{ inches} \end{eqnarray*}[/latex]
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
[latex]\begin{eqnarray*} H_0: & & \mu=5 \mbox{ years} \\ \\ H_a: & & \mu \lt 5 \mbox{ years} \end{eqnarray*}[/latex]
We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses.
[latex]\begin{eqnarray*} H_0: & & \mu=45 \mbox{ minutes} \\ \\ H_a: & & \mu \lt 45 \mbox{ minutes} \end{eqnarray*}[/latex]
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
[latex]\begin{eqnarray*} H_0: & & p=6.6\% \\ \\ H_a: & & p \gt 6.6\% \end{eqnarray*}[/latex]
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. State the null and alternative hypotheses.
[latex]\begin{eqnarray*} H_0: & & p=40\% \\ \\ H_a: & & p \gt 40\% \end{eqnarray*}[/latex]
In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we evaluate the null hypothesis , typically denoted with [latex]H_0[/latex]. The null hypothesis is not rejected unless the hypothesis test shows otherwise. The null hypothesis always contain an equal sign ([latex]=[/latex]). Always write the alternative hypothesis , typically denoted with [latex]H_a[/latex] or [latex]H_1[/latex], using less than, greater than, or not equals symbols ([latex]\lt[/latex], [latex]\gt[/latex], [latex]\neq[/latex]). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. But we can never state that a claim is proven true or false. All we can conclude from the hypothesis test is which of the hypothesis is most likely true. Because the underlying facts about hypothesis testing is based on probability laws, we can talk only in terms of non-absolute certainties.
“ 9.1 Null and Alternative Hypotheses “ in Introductory Statistics by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.
Introduction to Statistics Copyright © 2022 by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
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Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.
In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.
Null Hypothesis: H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis : H a : Male factory workers have a higher salary than female factory workers.
Null Hypothesis : H 0 : There is no relationship between height and shoe size. Alternative Hypothesis : H a : There is a positive relationship between height and shoe size.
Null Hypothesis : H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis : H a : The quality of a brick mason’s work is influenced by on-the-job experience.
All research starts with a problem that needs to be solved. From this problem, hypotheses are developed to provide the researcher with a clear statement of the problem.
To understand alternative hypotheses also known as alternate hypotheses, you must first understand what the hypothesis is .
When you hear the word hypothesis it means the accurate explanations in relation to a set of facts that can be analyzed when studied, using some specific method of research.
There are primarily two types of hypothesis which are null hypothesis and alternative hypothesis.
When you think about the word “null” what should come to mind is something that can not change, what you expect is what you get, unlike alternate hypotheses which can change.
Now, the research problems or questions which could be in the form of null hypothesis or alternative hypothesis are expressed as the relationship that exists between two or more variables. The process for this states that the questions should be what expresses the relationship between two variables that can be measured.
Both null hypotheses and alternative hypotheses are used by statisticians and researchers to conduct research in various industries or fields such as mathematics, psychology, science, medicine, and technology.
We are going to discuss alternative hypotheses and null hypotheses in this post and how they work in research.
Alternative hypothesis simply put is another viable option to the null hypothesis. It means looking for a substantial change or option that can allow you to reject the null hypothesis.
It is an opposing theory to a null hypothesis.
If you develop a null hypothesis, you make an informed guess on whether a thing is true or whether there is a relationship between that thing and another variable. An alternate hypothesis will always take an opposite stand against a null hypothesis. So if according to a null hypothesis something is correct to an alternate hypothesis that same thing will be incorrect.
For example, let’s assume that you develop a null hypothesis that states “I”m going to be $500 richer” the alternate hypothesis will be “I’m going to get $500 or be richer”
When you are trying to disprove a null hypothesis, that is when you test an alternate hypothesis. If there is enough data to back up the alternative hypothesis then you can dispose of the null hypothesis.
Get Answers: What is Empirical Research Study? [Examples & Method]
The null hypothesis is best explained as the statement showing that no relationship exists between two variables that are being considered or that two groups are not related. As we have earlier established, a hypothesis is an assumed statement that has not been proven with sufficient data that could serve as a piece of evidence.
The null hypothesis is now the statement that a researcher or an investigator wants to disprove. The null hypothesis is capable of being tested, being verifiable, and also capable of being rejected.
For example, if you want to conduct a study that will compare the relationship between project A and project B if the study is based on the assumption that both projects are of equal standard, the assumption is referred to as the null hypothesis.
This is because the null hypothesis should be specific at all times.
Learn: Hypothesis Testing in Research: Definition, Procedure, Uses, Limitations + Examples
For the curious: Sampling Bias: Definition, Types + [Examples]
Here are the purposes of the null hypothesis in an experiment or study:
Now, these are the principles of the null hypothesis:
1. The primary principle of the null hypothesis is to prove that the assumed statement is true. This is done by collecting data and analyzing in the study , what chance the collected data has in the random sample.
2. If the collected data does not meet the expectation of the null hypothesis, it is determined that the data lacks sufficient evidence to back up the null hypothesis therefore the null hypothesis statement is rejected.
Just as in the case of the alternative hypothesis the collected data in a null hypothesis is analyzed using some statistical tools that are made to measure the extent to which data left the null hypothesis.
The process will determine whether the data that left the null hypothesis is larger than a set value. If the data collected from the random sample is enough to serve as evidence to prove the null hypothesis then the null hypothesis will be accepted as true. And also defined that it has no relationship with other variables .
Learn About: Research Reports: Definition, Types + [Writing Guide]
There are four types of alternative hypotheses, and we will briefly discuss them below.
Read: Type I vs Type II Errors: Definition, Examples & Prevention
We are going to look at the differences between the alternate hypothesis and the null hypothesis based on these six factors which are:
Null hypothesis is followed by an ‘equals to’ (=) sign. While the Alternative hypothesis is followed by these three signs;
In the null hypothesis, it is believed that the results that are observed are as a result of chance. While In the alternative hypothesis, it is believed that the observed results are the outcome of some real causes.
The result of the null hypothesis always shows that there have been no changes in statements or opinions. While the result of the alternative hypothesis shows that there have been significant changes in statements and opinions.
If the p-value in a null hypothesis is greater than the significance level, then the null hypothesis is accepted.
If the p-value in an alternate hypothesis is smaller than the significance level, then the alternative hypothesis is accepted.
The null hypothesis accepts true existing theories and also if there has been consistency in multiple experiments of similar hypotheses.
The alternative hypothesis establishes whether a relationship exists between two variables, and the result will then lead to new improved theories.
Read: T-testing: Definition, Formula & Interpretations
Here are some examples of the alternative hypothesis:.
A researcher assumes that a bridge’s bearing capacity is over 10 tons, the researcher will then develop an hypothesis to support this study. The hypothesis will be:
For the null hypothesis H0: µ= 10 tons
For the alternate hypothesis Ha: µ>10 tons
In another study being conducted, the researcher wants to find out whether there is a noticeable difference or change in a patient’s heart arrest medicine and the patient’s heart condition.
For the alternate hypothesis: The hypothesis is that there might indeed be a relationship between the new medicine and the frequency or chances of heart arrest in a patient.
The hypothesis from example 2 in the alternate hypothesis implies that the use of one specific medicine can reduce the frequency and chances of heart arrest.
For the null hypothesis: The hypothesis will be that the use of that particular medicine cannot reduce the chance and frequency of heart arrest in a patient.
An alternate hypothesis states that the random exam scores are collected from both men and women. But are the scores of the two groups (men and women) the same or are they different?
For the null hypothesis: The hypothesis will state that the calculated mean of the men’s exam score is equal to the exam score of the women.
This is represented as
H0= The null hypothesis
µ1= The calculated mean score of men
µ2= The calculated mean score of women
Read: What is Empirical Research Study? [Examples & Method]
It is quite inappropriate to say or report that an alternate hypothesis was rejected. It is much better to use the phrase “the alternate hypothesis was rather not supported”.
The reason behind this use of words is that only the null hypothesis is designed to be rejected in a study. The alternative hypothesis is designed to prove the null hypothesis incorrect, to introduce new facts that can disprove the null hypothesis but it is not designed to be rejected.
It can either be accepted or not supported.
A researcher can use this formula to identify the alternate hypothesis in a study or experiment.
H0 and Ha are in contrast.
Therefore, if Ho has:
Equal to (=)
Greater than or equal to (≥)
Less than or equal to (≤)
And then Ha has:
Not equal (≠)
Greater than (>) or less than (
Less than ( )
If in a study, α ≤ p-value, then the researcher should not reject H0.
If in a study, α > p-value, then the researcher should reject H0.
α is preconceived. The value of α is determined even before the hypothesis test is conducted. While the p-value is derived from the calculation in the data.
The study a researcher wants to conduct will determine what hypothesis should be developed. However, the researcher should keep in mind what the purpose of the null and alternative two hypotheses are while developing the study hypothesis. So while the null hypothesis will accept existing theories that it found to be true or correct, and measure the consistency of multiple experiments, alternative hypotheses will find the relationship that exists (if any) between two phenomena and may lead to the development of a new and improved theory.
In this article, it has been clearly defined the relationship that exists between the null hypothesis and the alternative hypothesis. While the null hypothesis is always an assumption that needs to be proven with evidence for it to be accepted, the alternative hypothesis puts in all the effort to make sure the null hypothesis is disproved.
Researchers should note that for every null hypothesis, one or more alternate hypotheses can be developed.
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In this article we’ll look at the different types and characteristics of extrapolation, plus how it contrasts to interpolation.
In this post, we will discuss extensively what acceptance sampling is and when it is applied.
This article will discuss the two different types of errors in hypothesis testing and how you can prevent them from occurring in your research
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The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups.
The following are some examples of null hypothesis:
H 0 : µ 1 = µ 2
H 0 = null hypothesis µ 1 = mean score of men µ 2 = mean score of women
An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study.
The following are some examples of alternative hypothesis:
1. If a researcher is assuming that the bearing capacity of a bridge is more than 10 tons, then the hypothesis under this study will be:
Null hypothesis H 0 : µ= 10 tons Alternative hypothesis H a : µ>10 tons
2. Under another study that is trying to test whether there is a significant difference between the effectiveness of medicine against heart arrest, the alternative hypothesis will be that there is a relationship between the medicine and chances of heart arrest.
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. | An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. | |
It is denoted by H . | It is denoted by H or H . | |
It is followed by ‘equals to’ sign. | It is followed by not equals to, ‘less than’ or ‘greater than’ sign. | |
The null hypothesis believes that the results are observed as a result of chance. | The alternative hypothesis believes that the results are observed as a result of some real causes. | |
It is the hypothesis that the researcher tries to disprove. | It is a hypothesis that the researcher tries to prove. | |
The result of the null hypothesis indicates no changes in opinions or actions. | The result of an alternative hypothesis causes changes in opinions and actions. | |
If the null hypothesis is accepted, the results of the study become insignificant. | If an alternative hypothesis is accepted, the results of the study become significant. | |
If the p-value is greater than the level of significance, the null hypothesis is accepted. | If the p-value is smaller than the level of significance, an alternative hypothesis is accepted. | |
The null hypothesis allows the acceptance of correct existing theories and the consistency of multiple experiments. | Alternative hypothesis are important as it establishes a relationship between two variables, resulting in new improved theories. |
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Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different.
How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference.
The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H 0 .
The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.
If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.
For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit . The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has a temperature of 98.6 degrees. We do not prove that this is true.
If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.
The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either H a or by H 1 .
The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis. Going back to the above example of mean human body temperature, the alternative hypothesis is “The average adult human body temperature is not 98.6 degrees Fahrenheit.”
If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.
The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook.
What is the null hypothesis, how to state the null hypothesis, null hypothesis overview.
The word “null” in this context means that it’s a commonly accepted fact that researchers work to nullify . It doesn’t mean that the statement is null (i.e. amounts to nothing) itself! (Perhaps the term should be called the “nullifiable hypothesis” as that might cause less confusion).
The short answer is, as a scientist, you are required to ; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.
Several scientists, including Copernicus , set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the Flat Earth Society !. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong .
You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis . Breaking your problem into a few small steps makes these problems much easier to handle.
Step 2: Convert the hypothesis to math . Remember that the average is sometimes written as μ.
H 1 : μ > 8.2
Broken down into (somewhat) English, that’s H 1 (The hypothesis): μ (the average) > (is greater than) 8.2
Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.
H 0 : μ ≤ 8.2
Broken down again into English, that’s H 0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2
But what if the researcher doesn’t have any idea what will happen.
Example Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks.
Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.
H 0 : μ = 8.2
Broken down into English, that’s H 0 (The null hypothesis): μ (the average) = (is equal to) 8.2
Step 2: Figure out the alternate hypothesis . The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?
H 1 : μ ≠ 8.2
In English again, that’s H 1 (The alternate hypothesis): μ (the average) ≠ (is not equal to) 8.2
That’s How to State the Null Hypothesis!
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Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley.
Often in statistics we want to test whether or not some assumption is true about a population parameter .
For example, we might assume that the mean weight of a certain population of turtle is 300 pounds.
To determine if this assumption is true, we’ll go out and collect a sample of turtles and weigh each of them. Using this sample data, we’ll conduct a hypothesis test .
The first step in a hypothesis test is to define the null and alternative hypotheses .
These two hypotheses need to be mutually exclusive, so if one is true then the other must be false.
These two hypotheses are defined as follows:
Null hypothesis (H 0 ): The sample data is consistent with the prevailing belief about the population parameter.
Alternative hypothesis (H A ): The sample data suggests that the assumption made in the null hypothesis is not true. In other words, there is some non-random cause influencing the data.
There are two types of alternative hypotheses:
A one-tailed hypothesis involves making a “greater than” or “less than ” statement. For example, suppose we assume the mean height of a male in the U.S. is greater than or equal to 70 inches.
The null and alternative hypotheses in this case would be:
A two-tailed hypothesis involves making an “equal to” or “not equal to” statement. For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches.
Note: The “equal” sign is always included in the null hypothesis, whether it is =, ≥, or ≤.
The following examples illustrate how to define the null and alternative hypotheses for different research problems.
Example 1: A biologist wants to test if the mean weight of a certain population of turtle is different from the widely-accepted mean weight of 300 pounds.
The null and alternative hypothesis for this research study would be:
If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean weight of this population of turtles is different from 300 pounds.
Example 2: An engineer wants to test whether a new battery can produce higher mean watts than the current industry standard of 50 watts.
If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean watts produced by the new battery is greater than the current industry standard of 50 watts.
Example 3: A botanist wants to know if a new gardening method produces less waste than the standard gardening method that produces 20 pounds of waste.
If we reject the null hypothesis, this means we have sufficient evidence from the sample data to say that the true mean weight produced by this new gardening method is less than 20 pounds.
Whenever we conduct a hypothesis test, we use sample data to calculate a test-statistic and a corresponding p-value.
If the p-value is less than some significance level (common choices are 0.10, 0.05, and 0.01), then we reject the null hypothesis.
This means we have sufficient evidence from the sample data to say that the assumption made by the null hypothesis is not true.
If the p-value is not less than some significance level, then we fail to reject the null hypothesis.
This means our sample data did not provide us with evidence that the assumption made by the null hypothesis was not true.
Additional Resource: An Explanation of P-Values and Statistical Significance
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Know the Differences & Comparisons
Null hypothesis implies a statement that expects no difference or effect. On the contrary, an alternative hypothesis is one that expects some difference or effect. Null hypothesis This article excerpt shed light on the fundamental differences between null and alternative hypothesis.
Comparison chart.
Basis for Comparison | Null Hypothesis | Alternative Hypothesis |
---|---|---|
Meaning | A null hypothesis is a statement, in which there is no relationship between two variables. | An alternative hypothesis is statement in which there is some statistical significance between two measured phenomenon. |
Represents | No observed effect | Some observed effect |
What is it? | It is what the researcher tries to disprove. | It is what the researcher tries to prove. |
Acceptance | No changes in opinions or actions | Changes in opinions or actions |
Testing | Indirect and implicit | Direct and explicit |
Observations | Result of chance | Result of real effect |
Denoted by | H-zero | H-one |
Mathematical formulation | Equal sign | Unequal sign |
A null hypothesis is a statistical hypothesis in which there is no significant difference exist between the set of variables. It is the original or default statement, with no effect, often represented by H 0 (H-zero). It is always the hypothesis that is tested. It denotes the certain value of population parameter such as µ, s, p. A null hypothesis can be rejected, but it cannot be accepted just on the basis of a single test.
A statistical hypothesis used in hypothesis testing, which states that there is a significant difference between the set of variables. It is often referred to as the hypothesis other than the null hypothesis, often denoted by H 1 (H-one). It is what the researcher seeks to prove in an indirect way, by using the test. It refers to a certain value of sample statistic, e.g., x¯, s, p
The acceptance of alternative hypothesis depends on the rejection of the null hypothesis i.e. until and unless null hypothesis is rejected, an alternative hypothesis cannot be accepted.
The important points of differences between null and alternative hypothesis are explained as under:
There are two outcomes of a statistical test, i.e. first, a null hypothesis is rejected and alternative hypothesis is accepted, second, null hypothesis is accepted, on the basis of the evidence. In simple terms, a null hypothesis is just opposite of alternative hypothesis.
Zipporah Thuo says
February 22, 2018 at 6:06 pm
The comparisons between the two hypothesis i.e Null hypothesis and the Alternative hypothesis are the best.Thank you.
Getu Gamo says
March 4, 2019 at 3:42 am
Thank you so much for the detail explanation on two hypotheses. Now I understood both very well, including their differences.
Jyoti Bhardwaj says
May 28, 2019 at 6:26 am
Thanks, Surbhi! Appreciate the clarity and precision of this content.
January 9, 2020 at 6:16 am
John Jenstad says
July 20, 2020 at 2:52 am
Thanks very much, Surbhi, for your clear explanation!!
Navita says
July 2, 2021 at 11:48 am
Thanks for the Comparison chart! it clears much of my doubt.
GURU UPPALA says
July 21, 2022 at 8:36 pm
Thanks for the Comparison chart!
Enock kipkoech says
September 22, 2022 at 1:57 pm
What are the examples of null hypothesis and substantive hypothesis
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Table of Contents
A hypothesis test is a statistical method used to determine whether there is enough evidence to support or reject a hypothesis about a population. The conclusions of a hypothesis test are based on the analysis of sample data and can be either acceptance or rejection of the null hypothesis (the initial assumption) in favor of the alternative hypothesis. For example, if a researcher wants to test the hypothesis that students who study for longer hours score higher on exams, they would collect data from a sample of students and perform a hypothesis test. The conclusion of this test could be that there is enough evidence to support the hypothesis, or that there is not enough evidence to reject the null hypothesis. In this case, the researcher would conclude that there is a significant relationship between studying hours and exam scores, or that there is no significant difference between the two. The conclusions of a hypothesis test are crucial in determining the validity of a hypothesis and can help guide future research and decision-making .
A is used to test whether or not some hypothesis about a is true.
To perform a hypothesis test in the real world, researchers obtain a from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:
If the of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .
Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .
When writing the conclusion of a hypothesis test, we typically include:
For example, we would write:
We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…
Or, we would write:
We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…
The following examples show how to write a hypothesis test conclusion in both scenarios.
Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.
She then performs a hypothesis test at a 5% significance level using the following hypotheses:
Suppose the p-value of the test turns out to be 0.002.
We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.
Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.
He performs a hypothesis test at a 10% significance level using the following hypotheses:
Suppose the p-value of the test turns out to be 0.27.
Here is how he would report the results of the hypothesis test:
We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.
The following tutorials provide additional information about hypothesis testing:
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COMMENTS
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.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
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.
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
Alternative Hypothesis H A: The correlation in the population is not zero: ρ ≠ 0. For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis. The preceding examples are all for two-tailed hypothesis tests.
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
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.
10.1 - Setting the Hypotheses: Examples. A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or ...
The Null and Alternative Hypotheses. There are two hypotheses that are made: the null hypothesis, denoted H 0, and the alternative hypothesis, denoted H 1 or H A. The null hypothesis is the one to be tested and the alternative is everything else. In our example: The null hypothesis would be: The mean data scientist salary is 113,000 dollars.
Present the findings in your results and discussion section. Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps. Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test.
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.
The alternative hypothesis (H a H_a H a or H 1 H_1 H 1 ) is the hypothesis being proposed in opposition to the null hypothesis. Examples of Null and Alternative Hypotheses In a hypothesis test, the null and alternative hypotheses must be mutually exclusive statements, meaning both hypotheses cannot be true at the same time.
The null hypothesis is a claim that a population parameter equals some value. For example, H 0: μ = 5 H 0: μ = 5. The alternative hypothesis is denoted H a H a. It is a claim about the population that is contradictory to the null hypothesis and is what we conclude is true when we reject H 0 H 0. The alternative hypothesis is a claim that a ...
To distinguish it from other hypotheses, the null hypothesis is written as H 0 (which is read as "H-nought," "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95% or 99% is common. Keep in mind, even if the confidence level is high, there is still a small chance the ...
Examples: Null Hypothesis: H 0: There is no difference in the salary of factory workers based on gender. Alternative Hypothesis: H a: Male factory workers have a higher salary than female factory workers. Null Hypothesis: H 0: There is no relationship between height and shoe size. Alternative Hypothesis: H a: There is a positive relationship ...
Here are some examples of the alternative hypothesis: Example 1. A researcher assumes that a bridge's bearing capacity is over 10 tons, the researcher will then develop an hypothesis to support this study. The hypothesis will be: For the null hypothesis H0: µ= 10 tons. For the alternate hypothesis Ha: µ>10 tons.
The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups. An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study. Symbol. It is denoted by H 0.
Alternative hypothesis " x is not equal to y .". Null hypothesis: " x is at least y .". Alternative hypothesis " x is less than y .". Null hypothesis: " x is at most y .". Alternative hypothesis " x is greater than y .". Here are the differences between the null and alternative hypotheses and how to distinguish between them.
Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is "I expect the average recovery period to be greater than 8.2 weeks.". Step 2: Convert the hypothesis to math.
The alternative hypothesis ( Ha H a) is a claim about the population that is contradictory to H0 H 0 and what we conclude when we reject H0 H 0. Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample ...
Null hypothesis: µ ≥ 70 inches. Alternative hypothesis: µ < 70 inches. A two-tailed hypothesis involves making an "equal to" or "not equal to" statement. For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches. The null and alternative hypotheses in this case would be: Null hypothesis: µ = 70 inches.
A null hypothesis is what, the researcher tries to disprove whereas an alternative hypothesis is what the researcher wants to prove. A null hypothesis represents, no observed effect whereas an alternative hypothesis reflects, some observed effect. If the null hypothesis is accepted, no changes will be made in the opinions or actions.
In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements. "The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis. ... One example is ...
To perform a hypothesis test in the real world, researchers obtain a from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis: Null Hypothesis (H 0): The sample data occurs purely from chance. Alternative Hypothesis (H A): The sample data is influenced by some non-random cause.