Question: Suppose that the nine observations X1, . . . , X9 form a random sample from the normal distribution with unknown mean 1 and unknown

Suppose that the nine observations X1, . . . , X9 form a random sample from the normal with unknown mean μ1 and unknown variance σ2, and the nine observations Y1, . . . , Y9 form an independent random sample from the normal with unknown mean μ2 and the same unknown variance σ2. Let S2X and S2Y be as defined in Eq. (9.6.2) (with m = n = 9), and let
T = max {S2XS2Y/S2Y/S2X}.
Determine the value of the constant c such that Pr(T > c) = 0.05.

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