The principal would like to know if these data provide convincing evidence that the distribution of responses differs across the grades in the population of all students in her school. What is the appropriate inference procedure?

The question compares the distribution of a categorical response across several grade groups. Since the data come from independent random samples, the appropriate procedure is a chi-square test for homogeneity, which checks whether those population distributions are the same. A goodness-of-fit test is for comparing one sample’s distribution with a specified distribution.

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