Solution: Suppose that X1,...,Xm form a random sample from
Chapter 9, Problem 15(choose chapter or problem)
Suppose that X1,...,Xm form a random sample from the normal distribution with unknown mean 1 and unknown variance 2 1, and that Y1,...,Yn form an independent random sample from the normal distribution with unknown mean 2 and unknown variance 2 2. Suppose also that it is desired to test the following hypotheses with the usual F test at the level of significance 0 = 0.05: H0: 2 1 2 2, H1: 2 1 > 2 2. Assuming that m = 16 and n = 21, show that the power of the test when 2 1 = 22 2 is given by Pr(V 1.1), where V is a random variable having the F distribution with 15 and 20 degrees of freedom.
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