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 7.78 points, and their standard deviation is 1.06 points. The two-tailed students average 7.64 points, and their standard deviation is 1.30 points. Required:
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.