For the samples summarized below, test the hypothesis, at $\alpha = 0.05$, that the two variance are different.
$\begin{array}{l|cc}
& \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample Std. Deviation } & 4.1 & 2.7 \
\text { Sample size } & 10 & 20
\end{array}$

A) Accept the hypothesis because the test value 2.31 is less than the critical value 2.35
B) Reject the hypothesis because the test value 2.31 is less than the critical value 2.88.
C) Accept the hypothesis because the test value 5.32 is greater than the critical value 2.77.
D) Reject the hypothesis because the test value 5.32 is greater than the critical value 2.42.

Question

For the samples summarized below, test the hypothesis, at $\alpha = 0.05$, that the two variance are different.
$\begin{array}{l|cc} 
& \text { Sample 1 } & \text { Sample 2 } \
\hline \text { Sample Std. Deviation } & 4.1 & 2.7 \
\text { Sample size } & 10 & 20
\end{array}$

A) Accept the hypothesis because the test value 2.31 is less than the critical value 2.35
B) Reject the hypothesis because the test value 2.31 is less than the critical value 2.88.
C) Accept the hypothesis because the test value 5.32 is greater than the critical value 2.77.
D) Reject the hypothesis because the test value 5.32 is greater than the critical value 2.42.

Quizplus · Accepted Answer

The test value (F-statistic) is calculated as the ratio of the variances (4.1^2 / 2.7^2 = 2.31). Since 2.31 is less than the critical value 2.88 for the F-distribution at $\alpha = 0.05$ with degrees of freedom (9, 19), we fail to reject the null hypothesis that the variances are equal.

For the Samples Summarized Below, Test the Hypothesis, At α=0.05\alpha = 0.05α=0.05

For the Samples Summarized Below, Test the Hypothesis, At $\alpha = 0.05$