In constructing a 95% interval estimate for the ratio of two population variances, $\sigma _ { 1 } ^ { 2 }$ / $\sigma _ { 2 } ^ { 2 }$ , two independent samples of sizes 30 and 40 are drawn from the populations. If the sample variances are 425 and 675, then the upper confidence limit is about:
A) 1.2215.
B) 0.3132.
C) 1.2656.
D) 0.3246.

Question

Quizplus · Accepted Answer

First, we need to calculate the F-statistic:

F = (s1^2 / s2^2)

F = (425 / 675)

F = 0.6296

Next, we need to find the critical values of F for a 95% confidence interval with degrees of freedom 29 and 39 (sample sizes - 1):

Lower critical value = 1 / F-distribution(39,29) = 1 / 2.127 = 0.4702

Upper critical value = F-distribution(29,39) = 1 / 0.4702 = 2.1244

Finally, we can find the upper confidence limit for the ratio of population variances:

Upper limit = s1^2 / (s2^2 * lower critical value)

Upper limit = 425 / (675 * 0.4702)

Upper limit = 1.2656

Therefore, the best choice is C, with an upper confidence limit of about 1.2656.

In Constructing a 95% Interval Estimate for the Ratio of Two