Question

A professor wants to make sure that two different versions of a test are equivalent. He decides to compare the variances of the test scores from each version. A sample of 14 scores on Version A has a sample variance of 3.362, while a sample of 23 scores from Version 8 has a sample variance of 1.328. Construct a 90 % confidence interval for the ratio of the population variances of the scores on the two versions of the test. Round the endpoints of the interval to four decimal places, if necessary.

Answer 1

To construct a 90% confidence interval for the ratio of the population variances of the scores on two versions of the test, use the F-distribution.

Step-by-step explanation:

To construct a 90% confidence interval for the ratio of the population variances of the scores on the two versions of the test, we can use the F-distribution. The formula for the confidence interval is:

CI = [ (s1^2 / s2^2) * (1/F(q2, q1)), (s1^2 / s2^2) * F(q1, q2) ]

Where s1^2 and s2^2 are the sample variances, and q1 and q2 are the degrees of freedom. In this case, s1^2 = 3.362, s2^2 = 1.328, q1 = n1 - 1 = 14 - 1 = 13, and q2 = n2 - 1 = 23 - 1 = 22.

Using the F-distribution table or a statistical software, we can find the critical values F(q1, q2) for the given 90% confidence level. Once we have these values, we can substitute them into the formula to calculate the confidence interval.