Final answer:
The athletic director would perform a hypothesis test to determine whether to reject or fail to reject the null hypothesis regarding the proportions of freshmen and seniors who exercise regularly.
Step-by-step explanation:
The athletic director at a large university compared the proportions of freshmen (1st year students) and seniors (4th year students) who exercise regularly. To determine whether to reject or fail to reject the null hypothesis, the athletic director would perform a hypothesis test based on the given data. By comparing the observed proportions of freshmen and seniors who exercise regularly, the director can calculate the p-value. If the p-value is less than the significance level (alpha), typically 0.05 or 0.01, the director would reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the p-value is greater than alpha, the director would fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis.