Based on the sample evidence below, we want to test the hypothesis that population A has a larger variance than population B. Sample A
Sample B
N
11
10
S²
12) 1
5

The test statistic for this problem equals

Question

Quizplus · Accepted Answer

We need to perform an F-test for equality of variances. Using the sample data:
Sample A variance = (SS1U1P12S1S1P0)/(n-1) = 12/10 = 1.2
Sample B variance = (SS1U1P1)/(n-1) = 5/9 ≈ 0.56
We now calculate the F-statistic:
F = (Sample A variance)/(Sample B variance) = 1.2/0.56 ≈ 2.14
Looking at the F-distribution table with 10 and 9 degrees of freedom, we find that the critical value for a significance level of 0.05 is approximately 3.00. Since our calculated F-statistic is less than the critical value, we fail to reject the null hypothesis that the population variances are equal. Therefore, we don't have sufficient evidence to support the hypothesis that population A has a larger variance than population B. The correct answer is C (F = 2.14).

Based on the Sample Evidence Below, We Want to Test