In comparing the two standard deviations below, what test value and degrees of freedom should be used in an $F$ test?
$\begin{array}{l|cc}
& \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Standard deviation } & 7 & 3 \
\text { Sample size } & 14 & 23
\end{array}$

A) test value = 2.33; d.f.N. = 14 and d.f.D. = 23
B) test value = 2.33; d.f.N. = 22 and d.f.D. = 13
C) test value = 5.44; d.f.N. = 13 and d.f.D. = 22
D) test value = 5.44; d.f.N. = 23 and d.f.D. = 14

Question

In comparing the two standard deviations below, what test value and degrees of freedom should be used in an $F$ test?
$\begin{array}{l|cc} 
& \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Standard deviation } & 7 & 3 \
\text { Sample size } & 14 & 23
\end{array}$

A) test value = 2.33; d.f.N. = 14 and d.f.D. = 23
B) test value = 2.33; d.f.N. = 22 and d.f.D. = 13
C) test value = 5.44; d.f.N. = 13 and d.f.D. = 22
D) test value = 5.44; d.f.N. = 23 and d.f.D. = 14

Quizplus · Accepted Answer

The test value for an $F$ test comparing two variances (or standard deviations) is calculated by dividing the larger variance by the smaller variance. Here, the variances are $7^2 = 49$ and $3^2 = 9$, so the test value is $49 / 9 = 5.44$. The degrees of freedom for the numerator (d.f.N.) is one less than the sample size of the group with the larger variance, which is $14 - 1 = 13$, and for the denominator (d.f.D.) is one less than the sample size of the group with the smaller variance, which is $23 - 1 = 22$.

In Comparing the Two Standard Deviations Below, What Test Value FFF

In Comparing the Two Standard Deviations Below, What Test Value $F$