(In some of the exercises that follow, we must make assumptions such as the exis

Question

(In some of the exercises that follow, we must make assumptions such as the existence of normal distributions with equal variances.) Say X and Y are independent random variables with distributions that are N(mu X, sigma 2X) and N(mu Y, sigma 2Y). We wish to test H0: sigma 2X = sigma 2Y against H1: sigma 2X > sigma 2Y. (a) Argue that, if H0 is true, the ratio of the two variances of the samples of sizes n and m, S2X/S2Y, has an F(n-1,m-1) distribution. (b) If n = m = 31, x = 8.153, s_x^2 = 1.410, y = 5.917 = 0.4399, s2x/s2y = 3.2053, and alpha = 0.01, show that H0 is rejected and H1 is accepted since 3.2053 > 2.39. (c) Where did the 2.39 come from?

Explanation / Answer

2.39 is the value of F dsitribution on 0.01 level of singificance and 30 degrees of freedom for both numerator and denominator

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