The chi-square distribution: introduction

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 test of independence hypothesis tests.

Introduction

Have you ever wondered if the number of sessions students spent in one-on-one tutoring in a year varied by the students' grade level in school? How about if the types of movies people preferred were different across different age groups? What about if there were differences in the major reasons various age groups used park trails? 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 one of the three major applications of the Chi-square distribution:

• The test of independence, which determines if events are independent, such as the examples above.

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.