# 11: The Chi-Square Distribution

- Page ID
- 20091

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A chi-squared test is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is true.

- 11.1: Introduction
- You will now study a new distribution, one that is used to determine the answers to such questions. This distribution is called the chi-square distribution.

- 11.2: Facts About the Chi-Square Distribution
- The chi-square distribution is a useful tool for assessment in a series of problem categories. These problem categories include primarily (i) whether a data set fits a particular distribution, (ii) whether the distributions of two populations are the same, (iii) whether two events might be independent, and (iv) whether there is a different variability than expected within a population.

- 11.3: Goodness-of-Fit Test
- In this type of hypothesis test, you determine whether the data "fit" a particular distribution or not. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test (meaning the distribution for the hypothesis test is chi-square) to determine if there is a fit or not. The null and the alternative hypotheses for this test may be written in sentences or may be stated as equations or inequalities.

- 11.4: Test of Independence
- Tests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test.

- 11.E: The Chi-Square Distribution (Exercises)
- These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/30189442-699...b91b9de@18.114.