Answer: chi-square distributed.

## Explanation In tests of independence for contingency table data, the appropriate nonparametric test statistic follows a **chi-square distribution**. ### Key Points: 1. **Contingency Table Tests**: When analyzing categorical data arranged in contingency tables (cross-tabulations), we use the chi-square test of independence. 2. **Test Statistic**: The test statistic is calculated as: $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$ where $O_i$ are observed frequencies and $E_i$ are expected frequencies under the null hypothesis of independence. 3. **Distribution**: Under the null hypothesis, this test statistic follows a chi-square distribution with degrees of freedom equal to $(r-1)(c-1)$, where $r$ is the number of rows and $c$ is the number of columns in the contingency table. ### Why Not Other Options: - **F-distributed (A)**: F-distribution is used in ANOVA tests and regression analysis, not for contingency table independence tests. - **Normally distributed (B)**: Normal distribution is used for parametric tests like z-tests, not for nonparametric contingency table tests. ### Application: This test is commonly used to determine whether there is a significant association between two categorical variables, such as testing whether gender is independent of voting preference, or whether product preference is independent of age group.

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