Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. The test statistic for this problem equals
A) .4132.
B) 1.1.
C) 2.42.
D) 2.

Question

Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B.  ​ The test statistic for this problem equals
A) .4132. 
B) 1.1. 
C) 2.42. 
D) 2.

Quizplus · Accepted Answer

Without any information on the sample mean, we can use the F-test to compare the variances of two populations. The test statistic is calculated as the ratio of the sample variances: F = s1^2/s2^2. In this case, we don't have the sample variances, but we do know the sample standard deviations, so we can square those to get the variances. (Note: it is assumed that the samples come from normal distributions and are independent.)

Population A: s1 = 5.5, n1 = 10, so s1^2 = 30.25
Population B: s2 = 3.2, n2 = 15, so s2^2 = 10.24

Therefore, F = 30.25/10.24 = 2.95

Looking up the critical value for a 0.05 significance level and degrees of freedom (9, 14) in an F-table, we find a value of 2.42. Since our calculated F-value is greater than the critical value, we reject the null hypothesis and conclude that population A has a larger variance than population B. The correct answer is C) 2.42.

Based on the Sample Evidence Below, We Want to Test