Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test.
A) test value = 2.94; d.f.N. = 26 and d.f.D. = 14
B) test value = 0.58; d.f.N. = 25 and d.f.D. = 13
C) test value = 1.71; d.f.N. = 25 and d.f.D. = 13
D) test value = 1.31; d.f.N. = 26 and d.f.D. = 14

Question

Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test. 
A) test value = 2.94; d.f.N. = 26 and d.f.D. = 14 
B) test value = 0.58; d.f.N. = 25 and d.f.D. = 13 
C) test value = 1.71; d.f.N. = 25 and d.f.D. = 13 
D) test value = 1.31; d.f.N. = 26 and d.f.D. = 14

Quizplus · Accepted Answer

The F test value is calculated by dividing the larger variance by the smaller variance. In this case, we do not have the actual values of the variances, but we can determine which one is larger based on the degrees of freedom. The numerator degrees of freedom (d.f.N.) should correspond to the sample with the larger variance, and the denominator degrees of freedom (d.f.D.) should correspond to the sample with the smaller variance. Based on this, we can see that the larger variance comes from the sample with 25 degrees of freedom, so d.f.N. = 25. The smaller variance comes from the sample with 13 degrees of freedom, so d.f.D. = 13. Therefore, we divide the larger variance by the smaller variance as follows: F = variance of larger sample / variance of smaller sample = (d.f.N. for larger sample / d.f.D. for smaller sample) = (25/13). The only choice that matches this calculation is C, which has a test value of 1.71 and d.f.N. = 25 and d.f.D. = 13.

Given the Variances of the Two Samples Below, Find the Test