In constructing a 90% interval estimate for the ratio of two population variances, / , two independent samples of sizes 40 and 60 are drawn from the populations. The sample variances are 515 and 920. What is the lower confidence limit?
A) 0.341
B) 0.352
C) 0.890
D) 0.918

Question

In constructing a 90% interval estimate for the ratio of two population variances,  /  , two independent samples of sizes 40 and 60 are drawn from the populations. The sample variances are 515 and 920. What is the lower confidence limit?
A) 0.341 
B) 0.352 
C) 0.890 
D) 0.918

Quizplus · Accepted Answer

We use the formula:

(F1/F2)*(Upper limit) < σ1^2/σ2^2 < (F1/F2)*(Lower limit)

where F1 = sample variance of the first sample/degrees of freedom of the first sample and F2 = sample variance of the second sample/degrees of freedom of the second sample.

Using the given values:

F1 = 515/39 = 13.205 
F2 = 920/59 = 15.593

From the F distribution table with 39 and 59 degrees of freedom and α = 0.1, the critical values are 0.559 and 1.696.

Plugging in the values:

(13.205/15.593)*0.559 < σ1^2/σ2^2 < (13.205/15.593)*1.696

0.336 < σ1^2/σ2^2 < 0.718

Taking the square roots:

0.579 < σ1/σ2 < 0.848

The lower confidence limit is 0.579.

In Constructing a 90% Interval Estimate for the Ratio of Two