Question: Question 5 Suppose that X1, ... , Xn form an i.i.d. random sample from the normal distri- bution with unknown mean and unknown variance, and

Question 5 Suppose that X1, ... , Xn form an i.i.d.

Question 5 Suppose that X1, ... , Xn form an i.i.d. random sample from the normal distri- bution with unknown mean and unknown variance, and let the random variable I denote the length of the shortest 1 - a confidence interval for the mean that can be constructed from the observed values in the sample. Find an expression for E(L) and compute its value for the sample size n = 10 and the confidence coefficient a = 0.05. Furthermore, discuss the relationship between 1. the expected value of the squared length E(L2) and the sample size n (all other parameters being fixed), 2. the expected value of the squared length E(L) and the confidence coeffi- cient a (all other parameters being fixed). Question 5 Suppose that X1, ... , Xn form an i.i.d. random sample from the normal distri- bution with unknown mean and unknown variance, and let the random variable I denote the length of the shortest 1 - a confidence interval for the mean that can be constructed from the observed values in the sample. Find an expression for E(L) and compute its value for the sample size n = 10 and the confidence coefficient a = 0.05. Furthermore, discuss the relationship between 1. the expected value of the squared length E(L2) and the sample size n (all other parameters being fixed), 2. the expected value of the squared length E(L) and the confidence coeffi- cient a (all other parameters being fixed)

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