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.
$\begin{array}{l|cc}
& \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Variance } & 7 & 11 \
\text { Sample size } & 14 & 26
\end{array}$

A) test value = 1.25; d.f.N. = 26 and d.f.D. = 14
B) test value = 0.64; d.f.N. = 25 and d.f.D. = 13
C) test value = 2.47; d.f.N. = 26 and d.f.D. = 14
D) test value = 1.57; d.f.N. = 25 and d.f.D. = 13

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.
$\begin{array}{l|cc} 
& \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Variance } & 7 & 11 \
\text { Sample size } & 14 & 26
\end{array}$

A) test value = 1.25; d.f.N. = 26 and d.f.D. = 14
B) test value = 0.64; d.f.N. = 25 and d.f.D. = 13
C) test value = 2.47; d.f.N. = 26 and d.f.D. = 14
D) test value = 1.57; d.f.N. = 25 and d.f.D. = 13

Quizplus · Accepted Answer

The test value for an F test is calculated by dividing the larger variance by the smaller variance. Here, it is $11 / 7 = 1.57$. The degrees of freedom (d.f.) for the numerator (N) is one less than the sample size of the group with the larger variance, so $26 - 1 = 25$, and for the denominator (D) it is one less than the sample size of the group with the smaller variance, so $14 - 1 = 13$.

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