Let S2X and S2Y be the respective variances of two
Let S2X and S2Y be the respective variances of two independent random samples of sizes n and m from N(μX, σ2X) and N(μY, σ2Y). Use the fact that F = [S2Y/σ2Y]/[S2X/σ2X] has an F distribution, with parameters r1 = m− 1 and r2 = n− 1, to rewrite P(c ≤ F ≤ d) = 1−α, where c = F1−α/2(r1, r2) and d = Fα/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, σ2X/σ2Y, is [0.41, 10.49], so that [0.64, 3.24] is a 98% confidence interval for σX/σY.
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