A statistics instructor who teaches a lecture section of 160 students wants to determine whether students have more difficulty with one-tailed hypothesis tests or with two-tailed hypothesis tests. On...

A statistics instructor who teaches a lecture section of 160 students wants to determine whether students have more difficulty with one-tailed hypothesis tests or with two-tailed hypothesis tests. On the next exam, 80 of the students, chosen at random, get a version of the exam with a 10-point question that requires a one-tailed test. The other 80 students get a question that is identical except that it requires a two-tailed test. The one-tailed students average 7.79 points, and their standard deviation is 1.06 points. The two-tailed students average 7.64 points, and their standard deviation is 1.31 points.

a. Can you conclude that the mean score μ1 on one tailed hypothesis test questions is higher than the mean score μ2 on two-tailed hypothesis test questions? State the appropriate null and alternate hypotheses, and then compute the P-value.

b. Can you conclude that the mean score μ1 on one tailed hypothesis test questions differs from the mean score μ2 on two-tailed hypothesis test questions? State the appropriate null and alternate hypotheses, and then compute the P-value.