Let X be a random variable with continuous distribution function F(x; 0), and you wish to test Ho: 0 = 00. (a) (5 points) Show that the test that rejects H, 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; 6) is the distribution function of a sample mean X from iid N(u, o2), 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 or 2 > 1.96, where Z= X/o). (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 = 00, and show that you get the usual confidence interval (X 1.960/Vn, + 1.960/Vn)