Problem 1. Suppose that X1, . . . ,Xn are an i.i.d. random sample of size n with sample mean X = 12 and sample variance 32 = 5. (a) Let n = 5 and suppose the samples are drawn from a Normal distribution with unknown mean pi and known variance 02 = 9. Let the null hypothesis be H0 : p = 10 and the alternative hypothesis be Ha : n % 10. Calculate the relevant test statistic value and pvalue. Determine the decision rule for a = 0.05. (b) Using the acceptance region of this test, construct a 95% condence interval. (Hint: Think about how we can reverse our hypothesis test to construct the equivalent 95% condence interval)