Suppose that X1, . . . , Xm form a random sample from the normal distribution with unknown mean μ1 and unknown variance σ21, and that Y1, . . . , Yn form an independent random sample from the normal distribution with unknown mean μ2 and unknown variance σ22. Suppose also that it is desired to test the following hypotheses with the usual F test at the level of significance α0 = 0.05:
H0: σ21 ≤ σ22,
H1: σ21 > σ22.
Assuming that m = 16 and n = 21, show that the power of the test when σ21 = 2σ22 is given by Pr(V∗ ≥ 1.1), where V∗ is a random variable having the F distribution with 15 and 20 degrees of freedom.