Let X1, X2, ..., X20 be a random sample from a N(0, 62) distribution. It is desired to construct a 95% confidence interval for 2 and to test Ho : 62 = 2 against H1 : 62 > 2 at the 0.05 level of significance. Note: The sample size is n = 20. 20 (a) Justify that the distribution of 0 = _ is a x30 distribution? (3) i=1 (b) Find a and b (a b). (4 ) 20 20 (c) Use parts (a) and (b) to show that ( 0.0293 x?, 0.1043 is a 95% confidence i=1 i=1 interval estimator for o2. Hint: What is P(a s Q s b)? 6) (d) Show that the uniformly most powerful test for Ho : 62 = 2 against H1 : 62 > 2, at the 20 2 0.05 level of significance, rejects Ho if Q => N .. 2 31.41. Note: The sample size is n = 20. (16)