Say X and Y are independent random variables with distributions that are N(X , 2 X ) and
Chapter 8, Problem 8.2-15(choose chapter or problem)
Say X and Y are independent random variables with distributions that are N(X , 2 X ) and N(Y , 2 Y ). We wish to test H0: 2 X = 2 Y against H1: 2 X > 2 Y . (a) Argue that, if H0 is true, the ratio of the two variances of the samples of sizes n and m, S2 X /S2 Y , has an F(n1, m1) distribution. (b) If n = m = 31, x = 8.153, s2 x = 1.410, y = 5.917, s2 y = 0.4399, s2 x/s2 y = 3.2053, and = 0.01, show that H0 is rejected and H1 is accepted since 3.2053 > 2.39. (c) Where did the 2.39 come from?
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