The Chi-Square Distribution

Summary :

This chapter uses examples such as whether lottery numbers are evenly distributed to introduce the chi-square distribution and its notation. It covers interpreting the chi-square probability distribution as sample size changes, and conducting and interpreting goodness-of-fit tests, tests of independence, tests of homogeneity, and single-variance tests.

Interpreting the chi-square distribution

The chapter teaches students to interpret the chi-square probability distribution as the sample size changes, establishing its notation and shape before applying it to four distinct hypothesis-testing situations, each suited to a different kind of categorical or variance question.

Goodness-of-fit and independence tests

Students learn to conduct and interpret chi-square goodness-of-fit hypothesis tests, which check whether data such as lottery number frequencies match an expected distribution, and chi-square tests of independence, which check whether two categorical variables, such as movie preference and age group, are related.

Homogeneity and single-variance tests

The chapter also covers chi-square homogeneity hypothesis tests, which compare distributions across several populations, and chi-square single-variance hypothesis tests, illustrated with whether a coffee machine dispenses a consistent amount, rounding out the four applications of the distribution covered in the chapter.