Let X1 , X2 ,... , Xn , be a random sample from a normal population, with unknown mean, and variance σ2 = 5. The population mean is to be estimated with the sample mean such that the 95% con?dence interval will be ξL ≤ μ - X¯ ξR, an interval of total width w = ξR - ξL.

(i) Determine the sample size n required for w = 0.5.

(ii) If the population variance doubles to σ2 = 10, what value of n will be required to maintain the same width for the 95% con?dence interval?

(iii) If the population variance doubles but the sample size obtained in (i) is retained, what is the width of the 95% con?dence interval?