Let xi, i = 1,2,...,n be independent realizations from apopulation distributed like a Pareto with unknown mean.
(a) Compute the Standard Error of the sample mean. [Note:By“computeâ€, I mean “find the formula forâ€]. What is theprobability that the sample mean is two standard deviations largerthan the popula-
tion mean?
(b) Suppose the sample mean is 1 and the Standard Error is 2.Con- sider a test of the hypothesis that the population mean is 0,against the alternative that it is greater. What is the p−value?Compute a 5% confidence interval [Note: Use the Normal as anapprox- imation for simplicity]. What is the type II error if theactual population mean is 2?
