Test Hypotheses Regarding Two Population Standard Deviations
-Test the hypothesis that $\sigma _ { 1 } \neq \sigma _ { 2 }$ at the $\alpha = 0.05$ level of significance for the given sample data.
$\begin{array}{c|cc}
& \text { Population 1 } & \text { Population 2 } \
\hline \mathrm{n} & 16 & 13 \
\mathrm{~s} & 20.4 & 23
\end{array}$

A) Test statistic: $F = 0.79$. Critical values $= 0.338,3.18$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 0.79$. Critical values $= 0.314,3.18$. Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 0.79$. Critical values $= 0.338$, 3.18. Reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 0.79$. Critical values $= 0.403,2.62$. Reject $\mathrm { H } _ { 0 }$.

Question

Test Hypotheses Regarding Two Population Standard Deviations
-Test the hypothesis that $\sigma _ { 1 } \neq \sigma _ { 2 }$ at the $\alpha = 0.05$ level of significance for the given sample data.
$\begin{array}{c|cc} 
& \text { Population 1 } & \text { Population 2 } \
\hline \mathrm{n} & 16 & 13 \
\mathrm{~s} & 20.4 & 23
\end{array}$

A) Test statistic: $F = 0.79$. Critical values $= 0.338,3.18$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 0.79$. Critical values $= 0.314,3.18$. Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 0.79$. Critical values $= 0.338$, 3.18. Reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 0.79$. Critical values $= 0.403,2.62$. Reject $\mathrm { H } _ { 0 }$.

Quizplus · Accepted Answer

The test statistic $F$ is calculated by dividing the variance (square of the standard deviation) of one sample by the variance of the other. Given the standard deviations, $F = \frac{20.4^2}{23^2} = 0.79$. The correct critical values for an F-test with these sample sizes (n1 = 16, n2 = 13) at $\alpha = 0.05$ are indeed 0.338 and 3.18. Since the F value is within the range of the critical values, we do not reject the null hypothesis $\mathrm { H } _ { 0 }$, which posits that the population variances are equal ($\sigma _ { 1 }^2 = \sigma _ { 2 }^2$), or equivalently, the standard deviations are equal ($\sigma _ { 1 } = \sigma _ { 2 }$).

Test Hypotheses Regarding Two Population Standard Deviations -Test the Hypothesis σ1≠σ2\sigma _ { 1 } \neq \sigma _ { 2 }σ1​=σ2​

Test Hypotheses Regarding Two Population Standard Deviations
-Test the Hypothesis $\sigma _ { 1 } \neq \sigma _ { 2 }$