Consider a situation where there is a random sample of students who attend a public university and a study is conducted to determine whether the racial distribution of students is different from the racial distribution in the state as a whole.

Chi-square goodness-of-fit test is applied when there is one categorical variable selected from a single population. It tests whether the distribution of this single categorical variable follows the theoretical distribution.

In this situation, the sample was collected randomly. Each observation is independent of all other observations. It is also assumed that expected counts are large. As the hypothesis in this situation is to test whether true distribution of race (categorical variable) is different from proposed distribution, chi-square goodness-of-fit test is most appropriate.

Therefore, the appropriate test is Chi-square goodness-of-fit test.

Chi-square goodness-of-fit test is applied when there is one categorical variable selected from a single population. It tests whether the distribution of this single categorical variable follows the theoretical distribution.

In this situation, the sample was collected randomly. Each observation is independent of all other observations. It is also assumed that expected counts are large. As the hypothesis in this situation is to test whether true distribution of race (categorical variable) is different from proposed distribution, chi-square goodness-of-fit test is most appropriate.

Therefore, the appropriate test is Chi-square goodness-of-fit test.