Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo



This is a photo of a pile of grocery store receipts. The items and prices are blurred.
Figure 11.1 The chi-square distribution can be used to find relationships between two things, like grocery prices at different stores. (credit: Pete/flickr)

Chapter Objectives

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

  • 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 (see Appendix G Notes for the TI-83, 83+, 84, 84+ Calculators). TI-83+ and TI-84 calculator instructions are included in the text.

Collaborative Exercise

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.

Order a print copy

As an Amazon Associate we earn from qualifying purchases.


This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: . Changes were made to the original material, including updates to art, structure, and other content updates.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at
Citation information

© Jan 23, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.