Example 9.13

EXAMPLE 9.13 The Goodness-of-Fit Test for the ACT Study

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For Arizona, the observed count is 167. In Example 9.12, we calculated the expected count, 164.535. The contribution to the chi-square statistic for Arizona is

We use the same approach to find the contributions to the chi-square statistic for the other five states. The expected counts are all at least 5, so we can proceed with the significance test.

The sum of these six values is the chi-square statistic,

The degrees of freedom are the number of cells minus 1: . We calculate the P-value using Table F or software. From Table F, we can determine . We conclude that the observed counts are compatible with the hypothesized proportions. The data do not provide any evidence that our systematic sample was biased with respect to selection of subjects from different states.