Student 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 single variance hypothesis tests (optional).

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 fits 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 Chi-square calculations depend on calculators or computers for most of the calculations. TI-83+ and TI-84 calculator instructions are in the the chapter.

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.