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: Compares an observed distribution with an expected distribution for a single categorical variable from one sample. But here we have two categorical variables (attending game - yes/no and grade level).
• Chi - square test for homogeneity: Used when we have multiple independent samples (here, samples of 9th, 10th, 11th, and 12th graders) and we want to test if the distribution of a categorical variable (attending game - yes/no) is the same across these groups.
• Chi - square test for association/independence: Used when we have one sample and two categorical variables to test if there is an association between them. But here we have independent samples (by grade level).

Since we have independent random samples (by grade level) and we want to check if the distribution of the "attending game" variable is the same across these groups (grade levels), the chi - square test for homogeneity is appropriate.

Answer:

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