Let S2X and S2Y be the respective variances of two independent random samples of sizes n and m from N( Icirc frac14 X, Iuml 2X) and N( Icirc frac14 Y, Iuml 2Y) Use the fact that F S2Y Iuml 2Y S2X Iuml 2X has an F distribution, with parameters r1 m 1 and r2 n 1, to rewrite P(c curren F curren d) 1 I...

Where c F 12 r 1 r 2 1F 2 r 2 r 1 and d F 2 r 1 r 2 With ...

Let S2X and S2Y be the respective variances of two independent random samples of sizes n and

Question:

Let S2X and S2Y be the respective variances of two independent random samples of sizes n and m from N(Î¼X, Ïƒ2X) and N(Î¼Y, Ïƒ2Y). Use the fact that F = [S2Y/Ïƒ2Y]/[S2X/Ïƒ2X] has an F distribution, with parameters r1 = mˆ’ 1 and r2 = nˆ’ 1, to rewrite P(c ‰¤ F ‰¤ d) = 1ˆ’Î±, where c = F1ˆ’Î±/2(r1, r2) and d = FÎ±/2(r1, r2), so that

If the observed values are n = 13, m = 9, 12S2X = 128.41, and 8 s2y = 36.72, show that a 98% confidence interval for the ratio of the two variances, Ïƒ2X/Ïƒ2Y, is [0.41, 10.49], so that [0.64, 3.24] is a 98% confidence interval for ÏƒX/ÏƒY.