The chi-square distribution

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 preferredwere different across different age groups? What about if a coffee machine was dispensing approximately the same amount of coffee each time? You could answer thesequestions 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

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, swimmingtimes, 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 yourchoice.