A null hypothesis example

The next step is to formulate an analysis plan, which outlines how the data will be evaluated. The third step is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.

Analysts look to reject the null hypothesis because doing so is a strong conclusion. This requires strong evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that factors other than chance may be at work but may not be strong enough to be detectable by the statistical test used.

Analysts look to reject the null hypothesis to rule out chance alone as an explanation for the phenomena of interest. Here is a simple example. A school principal claims that students in her school score an average of 7 out of 10 in exams.

The null hypothesis is that the population mean is 7. To test this null hypothesis, we record marks of say 30 students sample from the entire student population of the school say and calculate the mean of that sample. We can then compare the calculated sample mean to the hypothesized population mean of 7. The null hypothesis here—that the population mean is 7. Assume that a mutual fund has been in existence for 20 years.

We take a random sample of annual returns of the mutual fund for, say, five years sample and calculate the sample mean. For the above examples, null hypotheses are:. For the purposes of determining whether to reject the null hypothesis, the null hypothesis abbreviated H 0 is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic e.

Then, if the sample average is outside of this range, the null hypothesis is rejected. An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative hypothesis H 1.

For the above examples, the alternative hypothesis would be:. In other words, the alternative hypothesis is a direct contradiction of the null hypothesis. As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock. The null hypothesis states that there is no difference between the two average returns, and Alice is inclined to believe this until she can conclude contradictory results.

Refuting the null hypothesis would require showing statistical significance, which can be found using a variety of tests. The alternative hypothesis would state that the investment strategy has a higher average return than a traditional buy-and-hold strategy.

One tool that can be used to determine the statistical significance of the results is the p-value. A p-value that is less than or equal to 0. If Alice conducts one of these tests, such as a test using the normal model, resulting in a significant difference between her returns and the buy-and-hold returns the p-value is less than or equal to 0.

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By Anne Marie Helmenstine, Ph. Anne Marie Helmenstine, Ph. Helmenstine holds a Ph. She has taught science courses at the high school, college, and graduate levels. Learn about our Editorial Process. Featured Video. Cite this Article Format. Helmenstine, Anne Marie, Ph. Null Hypothesis Definition and Examples. Independent Variable Definition and Examples. Understanding Simple vs Controlled Experiments. Dependent Variable Definition and Examples. What Are the Elements of a Good Hypothesis? How to Write an Abstract for a Scientific Paper.

Your Privacy Rights. Here is how to write the null and alternative hypotheses for this scenario:. 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.

To test this, she collects data on the proportion of students who graduated on time last year at the university. 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.

To test this, he goes out and surveys citizens on whether or not they support the law. Your email address will not be published. Skip to content Menu.