Hillary claims that the median starting salary of female science graduates is higher than that of the male science graduates. To test for his claim, a paired difference experiment is conducted to compare the starting salary of male and female science graduates who find jobs. Pairs are formed by choosing a male and female with the same major, who took similar courses with similar grades. A random sample ofn = 15 pairs is selected in this manner. Let X be the number of pairs with the starting salary of the male graduate higher than that of the female graduate among the 15 pairs. (a) Define 6, the parameter to be tested. [4] (b) State the null and alternate hypotheses for Hillary. [4] ((2) Hillary considers X as the test statistic and sets the rejection region as RR = {X S 5}. Calculate a, the probability of committing a type I error. [4] (d) Suppose that the true value of 6 = 0.4. Calculate [3, the probability of committing a type 11 error. [4] (e) Based on the a and I? obtained in (c) and (d), do you think this test is good enough in terms of power and the level of significance? Make a suggestion to Hillary so that both a and B can be reduced simultaneously. [4]