Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean μ and unknown variance σ2, and let the random variable L denote the length of the shortest confidence interval for μ that can be constructed from the observed values in the sample. Find the value of E(L2) for the following values of the sample size n and the confidence coefficient γ :
a. n = 5, γ = 0.95
b. n = 10, γ = 0.95
c. n = 30, γ = 0.95
d. n = 8, γ = 0.90
e. n = 8, γ = 0.95
f. n = 8, γ = 0.99