Question

a study is conducted in a large high school to determine if the proportion of students who plan to come to the upcoming football game differs across grades. a random sample of 50 ninth graders, 50 tenth graders, 50 eleventh graders, and 50 twelfth graders was selected. the responses are displayed in the table. 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? - chi - square test for goodness of fit because the data come from one random sample - chi - square test for homogeneity because the data come from independent random samples - chi - square test for association/independence because the data come from one random sample - chi - square test for association/independence because the data come from independent random samples

Explanation:

• Chi - square test for goodness of fit: Used when we have one categorical variable and we want to test if the distribution of frequencies in the sample fits a hypothesized distribution. Here, we have two categorical variables (grade level and attending game), so this is not the case.
• Chi - square test for association/independence: Used when we have one sample and we want to test if two categorical variables are related. But here, we have four independent samples (one from each grade level).
• Chi - square test for homogeneity: Used when we have multiple independent samples (in this case, samples from 9th, 10th, 11th, and 12th graders) and we want to test if the distribution of a categorical variable (attending the game: yes/no) is the same across these groups.

Answer:

chi - square test for homogeneity because the data come from independent random samples