Suppose that X1, , X11 form a random sample from the normal distribution with unknown mean 1 and unknown variance 21 Suppose also that Y1, , Y21 form an independent random sample from the normal distribution with unknown mean 2 and unknown variance 22 Suppose that we wish to test the hypotheses in Eq (9 7 7) Let be the equal tailed two sided F test with level of significance 0 0 5 a Compute the power function of when 21 1 0122 b Compute the power function of when 21 22 1 01 c Show that is not an unbiased test (You will probably need computer software that computes the function Gm1,n1 And try to minimize the amount of rounding you do )

Question: Suppose that X1, . . . , X11 form a random sample from the normal distribution with unknown mean 1 and unknown variance 21 .

Suppose that X1, . . . , X11 form a random sample from the normal with unknown mean μ1 and unknown variance σ21 . Suppose also that Y1, . . . , Y21 form an independent random sample from the normal with unknown mean μ2 and unknown variance σ22. Suppose that we wish to test the hypotheses in Eq. (9.7.7). Let δ be the equal-tailed two-sided F test with level of significance α0 = 0.5.
a. Compute the power function of δ when σ21 = 1.01σ22 .
b. Compute the power function of δ when σ21 = σ22 /1.01.
c. Show that δ is not an unbiased test. (You will probably need computer software that computes the function Gm−1,n−1. And try to minimize the amount of rounding you do.)

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