A test used to determine if observed frequencies across four categories match an expected distribution is called the chi-square goodness-of-fit test.

A test used to determine if observed frequencies across four categories match an expected distribution is called the chi-square goodness-of-fit test.

• A. Chi-square goodness of fit
• B. Chi-square test of independence
• C. ANOVA
• D. 2-proportion z-test

Answer: (A)

The main idea is to assess how well observed counts in several categories fit a specified distribution for a single categorical variable with multiple categories. You compare what you actually observe in each category to what you would expect under the null hypothesis, using the chi-square statistic: sum over categories of (O_i - E_i)^2 / E_i. A small value means the observed frequencies could reasonably come from the specified distribution; a large value suggests they do not. With four categories, the degrees of freedom are typically three if no parameters are estimated from the data. This approach is specifically for checking a single categorical distribution, not for relationships between variables or for comparing means. The other tests address different questions: independence in a contingency table, comparing means across groups, or comparing two proportions, respectively.

The main idea is to assess how well observed counts in several categories fit a specified distribution for a single categorical variable with multiple categories. You compare what you actually observe in each category to what you would expect under the null hypothesis, using the chi-square statistic: sum over categories of (O_i - E_i)^2 / E_i. A small value means the observed frequencies could reasonably come from the specified distribution; a large value suggests they do not. With four categories, the degrees of freedom are typically three if no parameters are estimated from the data. This approach is specifically for checking a single categorical distribution, not for relationships between variables or for comparing means. The other tests address different questions: independence in a contingency table, comparing means across groups, or comparing two proportions, respectively.