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The Chi-Square Distribution

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides an introduction to Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student Learning Outcomes

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.

Introduction

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 the above examples. 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 with the lottery example
  • The test of independence, which determines if events are independent, such as with the movie example
  • The test of a single variance, which tests variability, such as with the coffee example

Note:

Though the Chi-square calculations depend on calculators or computers for most of the calculations, there is a table available (see the Table of Contents 15. Tables). TI-83+ and TI-84 calculator instructions are included in the text.

Optional Collaborative Classroom Activity

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, etc.). 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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