Let X1, X2, . . . , X,. be a random sample from N(µ, er), where both parameters µ and u2 are unknown. A confidence interval for tr can be found as follows. We know that nS2/u 2 is x2(n - I ). Thus we can find constants a and b so that Pr (nS2/tr b) = 0.975 and Pr (a nS2/tr b) = 0.95.
(a) Show that this second probability statement can be written as Pr (nS2/b <>tr <>nS2/a) = 0.95.
(b) If n = 9 and s2 = 7.63, find a 95 percent confidence interval for u2.
(c) If µ is known, how would you modify the preceding procedure for finding a confidence interval for u2?