Question

a random sample of 175 students was selected from a large high school. they were each asked their current grade level and whether they had a drivers license. the responses are displayed in the table.

the principal would like to know if these data provide convincing evidence of a relationship between grade level and having a drivers license 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:

• A chi - square test for goodness of fit is used when we are comparing a single categorical variable's distribution to a hypothesized distribution. Here, we have two categorical variables (grade level and driver's license status), so this is not the case.
• A chi - square test for homogeneity is used when we have multiple independent samples and we want to compare the distribution of a categorical variable across these samples. But here we have one sample and two categorical variables.
• A chi - square test for association/independence is used to determine if there is a relationship between two categorical variables in a single sample. Since we have one random sample and we want to check the relationship between grade level (categorical) and driver's license status (categorical), this is the appropriate test.

Answer:

chi - square test for association/independence because the data come from one random sample.