5.9 What is the power of the test carried out in Problem 5.3? 5.10 Given the two hypotheses H0: μ = 400 H1: μ = 415 and σ2 = 1000 (for both hypotheses):

(a) Draw the distribution of X under both hypotheses.

(b) If the decision rule is chosen to be: reject H0 if X  410 from a sample of size 40, find the probability of a Type II error and the power of the test.

(c) What happens to these answers as the sample size is increased? Draw a diagram to illustrate.