2. Let X be a random variable with continuous distribution function F(x;0), and you wish to test Ho : 0 = 0o. (a) (5 points) Show that the test that rejects Ho if F(X;00) 0.975 has level 0.05. (b) (5 pts) Now apply the result in (a) to the setting where F(x; 0) is the distribution function of a sample mean X from iid N(u,02), where o2 is known. Show that the test in part (a) for testing Ho : 0 = 0 is the usual 2-tailed test rejecting H, if Z 1.96, where Z = X/(0/vn). (C) (5 points) Invert the test in part (b) by finding the set of 6, such that the test accepts the null hypothesis Ho: 0 = 0o, and show that you get the usual confidence interval (X - 1.960, X + 1.960)