The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.
-$\mathrm { s } _ { 1 } = 20.9 , \mathrm { n } _ { 1 } = 16 , \mathrm {~s} _ { 2 } = 22.2 , \mathrm { n } _ { 2 } = 13$; two-tailed test, $\alpha = 0.05$
A)Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.338,3.18$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.403,2.62$. Reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.338,3.18$. Reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.314,3.18$. Do not reject $\mathrm { H } _ { 0 }$.

Question

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.
-$\mathrm { s } _ { 1 } = 20.9 , \mathrm { n } _ { 1 } = 16 , \mathrm {~s} _ { 2 } = 22.2 , \mathrm { n } _ { 2 } = 13$; two-tailed test, $\alpha = 0.05$  
A)Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.338,3.18$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.403,2.62$. Reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.338,3.18$. Reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 0.89$. Critical values $= 0.314,3.18$. Do not reject $\mathrm { H } _ { 0 }$.

Quizplus · Accepted Answer

The F-test statistic is calculated by dividing the variance (square of the standard deviation) of one sample by the variance of the other. Given $s_1 = 20.9, s_2 = 22.2$, the F statistic is $(20.9/22.2)^2 = 0.89$. The critical values for a two-tailed test at $\alpha = 0.05$ with degrees of freedom $df_1 = n_1 - 1 = 15$ and $df_2 = n_2 - 1 = 12$ are approximately $0.338$ and $3.18$. Since the F statistic falls within the range of the critical values, we do not reject the null hypothesis $H_0$.

The Sample Standard Deviations and Sample Sizes Are Given for Independent