Suppose that X1,....,Xn form a random sample from a normal distribution for which both the mean m and variance s^2 are unknown.
Let the random variable L denote the length of the shortest confidence interval for m that can be constructed from the observed values in the sample.
Find the value of E(L^2) for the following values of the sample size n and the confidence coefficient y:
a. n = 5, y = 0.95 (Ans: 6.16 s^2)
b. n = 8, y = 0.90 (Ans:2.05 s^2)