Module 11: The Chi Square Distribution

Introduction: The Chi-Square Distribution

Barbara Illowsky & OpenStax et al.

This is a photo of a pile of grocery store receipts. The items and prices are blurred.
The chi-square distribution can be used to find relationships between two things, like grocery prices at different stores. (credit: Pete/flickr)

Learning Objectives

By the end of this chapter, the student should be able to:

  • Interpret the chi-square probability distribution as the sample size changes.
  • Conduct and interpret chi-square goodness-of-fit hypothesis tests.
  • Conduct and interpret chi-square test of independence hypothesis tests.
  • Conduct and interpret chi-square homogeneity hypothesis tests.
  • Conduct and interpret chi-square single variance hypothesis tests.

Have you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency? How about if the types of movies people preferred were different across different age groups? What about if a coffee machine was dispensing approximately the same amount of coffee each time? You could answer these questions by conducting a hypothesis test.

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.

In this chapter, you will learn the three major applications of the chi-square distribution:

the goodness-of-fit test, which determines if data fit a particular distribution, such as in the lottery example
the test of independence, which determines if events are independent, such as in the movie example
the test of a single variance, which tests variability, such as in the coffee example
Though the chi-square distribution depends on calculators or computers for most of the calculations, there is a table available. TI-83+ and TI-84 calculator instructions are included in the text.


Look in the sports section of a newspaper or on the Internet for some sports data (baseball averages, basketball scores, golf tournament scores, football odds, swimming times, and the like). Plot a histogram and a boxplot using your data. See if you can determine a probability distribution that your data fits. Have a discussion with the class about your choice.


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Introduction: The Chi-Square Distribution Copyright © 2018 by Barbara Illowsky & OpenStax et al. is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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