Let X equal the verbal score on the Graduate Record Examinations (GRE). Assume that the distribution of X is approximately N(, ). Suppose it is known that = 150. A philosophy professor claims that the verbal scores of philosophy majors is greater than 150. They plan to test their claim using a random sample of n = 9.

(a) Define the hypotheses to be tested.

(b) Define the test statistic and calculate its value given that a random sample yielded the scores

152, 156, 161, 147, 150, 162, 157, 166, 154

(c) Define the critical region for which = 0.05.

(d) Decide whether or not to reject the null hypothesis.

(e) What is your conclusion in terms of the original problem?