Test Hypotheses Regarding Two Population Standard Deviations
-$$\mathrm { s } _ { 1 } = 20.8 , \mathrm { n } _ { 1 } = 16 , \mathrm {~s} _ { 2 } = 23 , \mathrm { n } _ { 2 } = 13 \text {; left-tailed test, } \alpha = 0.10$$
Test the hypothesis that $\sigma _ { 1 }

Question

Test Hypotheses Regarding Two Population Standard Deviations
-$$\mathrm { s } _ { 1 } = 20.8 , \mathrm { n } _ { 1 } = 16 , \mathrm {~s} _ { 2 } = 23 , \mathrm { n } _ { 2 } = 13 \text {; left-tailed test, } \alpha = 0.10$$
Test the hypothesis that $\sigma _ { 1 } < \sigma _ { 2 }$ at the $\alpha = 0.10$ level of significance for the given sample data.
$\begin{array}{l|cc} 
& \text { Population 1 } & \text { Population 2 } \
\hline \mathrm{n} & 16 & 13 \
\mathrm{~s} & 20.8 & 23
\end{array}$

A) Test statistic: $\mathrm { F } = 0.82$. Critical value $= 0.495$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 0.82$. Critical value $= 0.476$. Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 0.82$. Critical value $= 0.495$. Reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 0.82$. Critical value $= 0.476$. Reject $\mathrm { H } _ { 0 }$.

Quizplus · Accepted Answer

The test statistic is calculated as:$$F = \frac{s_1^2}{s_2^2} = \frac{20.8^2}{23^2} = 0.82$$The critical value for a left-tailed test with $\alpha = 0.10$ and degrees of freedom $(n_1-1, n_2-1) = (16-1, 13-1) = (15, 12)$ is 0.495.Since the test statistic (0.82) is greater than the critical value (0.495), we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that $\sigma _ { 1 } < \sigma _ { 2 }$.

Test Hypotheses Regarding Two Population Standard Deviations - Test the Hypothesis That

Test Hypotheses Regarding Two Population Standard Deviations
- Test the Hypothesis That