# Question: 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.

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.

**View Solution:**## Answer to relevant Questions

Let X1, X2, . . . , X5 be a random sample of SAT mathematics scores, assumed to be N(μX, σ2), and let Y1, Y2, . . . , Y8 be an independent random sample of SAT verbal scores, assumed to be N(μY, σ2). If the following ...An environmental survey contained a question asking what respondents thought was the major cause of air pollution in this country, giving the choices “automobiles,” “factories,” and “incinerators.” Two versions ...When placed in solutions of varying ionic strength, paramecia grow blisters in order to counteract the flow of water. The following 60 measurements in microns are blister lengths: (a) Construct an ordered stem-and-leaf ...Using the cigarette data in Exercise 6.5-7, find 95% confidence intervals for α, β, and σ2 under the usual assumptions. In Exercise 6.5-7 In a mechanical testing lab, Plexiglass strips are stretched to failure. Let X equal the change in length in mm before breaking. Assume that the distribution of X is N(μ, σ2). We shall test the null hypothesis H0: μ = ...Post your question