PROBLEM 14E

Let X1,X2, . . . ,Xn be a random sample of size n from the normal distribution N(μ, σ2). Calculate the expected length of a 95% confidence interval for μ,assuming that n = 5 and the variance is

(a) known.

(b) unknown.

Hint: To find E(S), first determine

(See Exercise 6.4-14.)