SECTION 9.2 SUMMARY

• • The chi-square goodness-of-fit test is used to compare the sample distribution of a categorical variable from a population with a hypothesized distribution. The data for observations with possible outcomes are summarized as observed counts, in cells. The null hypothesis specifies probabilities for the possible outcomes.

• • The analysis of these data is similar to the analyses of two-way tables discussed in Section 9.1. For each cell, the expected count is determined by multiplying the total number of observations by the specified probability. The null hypothesis is tested by the usual chi-square statistic, which compares the observed counts, , with the expected counts. Under the null hypothesis, has approximately the distribution with .