In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? $$\begin{array} { | l | c | c | }
\hline & \text { Standard Deviation } & \text { Number of values } \
\hline \text { Sample 1 } & 7 & 17 \
\hline \text { Sample 2 } & 2 & 25 \
\hline
\end{array}$$
A) test value = 3.50, degrees of freedom = 17 and 25
B) test value = 3.50, degrees of freedom = 16 and 24
C) test value = 12.25, degrees of freedom = 17 and 25
D) test value = 12.25, degrees of freedom = 16 and 24

Question

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used? $$\begin{array} { | l | c | c | } 
\hline & \text { Standard Deviation } & \text { Number of values } \
\hline \text { Sample 1 } & 7 & 17 \
\hline \text { Sample 2 } & 2 & 25 \
\hline
\end{array}$$
A) test value = 3.50, degrees of freedom = 17 and 25
B) test value = 3.50, degrees of freedom = 16 and 24
C) test value = 12.25, degrees of freedom = 17 and 25
D) test value = 12.25, degrees of freedom = 16 and 24

Quizplus · Accepted Answer

The test value for comparing two standard deviations is calculated using the formula for the F-test: $ F = \frac{s_1^2}{s_2^2} $. Here, $ s_1 = 7 $ and $ s_2 = 2 $, so $ F = \frac{7^2}{2^2} = \frac{49}{4} = 12.25 $. The degrees of freedom are $ n_1 - 1 $ and $ n_2 - 1 $, which are 16 and 24, respectively.

In Comparing the Two Standard Deviations Below, What Is the Test