Question: A student group maintains that each day, the average student must travel for at least 25 minutes one way to reach college. The college admissions office obtained a random sample of 32 one-way travel times from students. The sample had a mean of 19.3 minutes and a standard deviation of 9.9 minutes. Does the admissions office have sufficient evidence to reject the students' claim? Use α = 0.01.

(a) State the appropriate null and alternative hypotheses.

Ho: μ 25 (=, >, <, )

Ha: μ 25

(ii) Find t. (Give your answer correct to two decimal places.)

(iii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence that the mean travel time is less than 25 minutes.

Reject the null hypothesis, there is significant evidence that the mean travel time is less than 25 minutes.

Fail to reject the null hypothesis, there is not significant evidence that the mean travel time is less than 25 minutes.

Fail to reject the null hypothesis, there is significant evidence that the mean travel time is less than 25 minutes.