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.
-$\mathrm { s } _ { 1 } = 5.85 , \mathrm { n } _ { 1 } = 31 , \mathrm {~s} _ { 2 } = 5.01 , \mathrm { n } _ { 2 } = 25$; two-tailed test, $\alpha = 0.10$
A)Test statistic: $\mathrm { F } = 1.17$. Critical values $= 0.515,1.94$. Reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 1.36$. Critical values $= 0.515,1.94$. Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 1.17$. Critical values $= 0.529,1.94$. Do not reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 1.36$. Critical values $= 0.529,1.94$. 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.
-$\mathrm { s } _ { 1 } = 5.85 , \mathrm { n } _ { 1 } = 31 , \mathrm {~s} _ { 2 } = 5.01 , \mathrm { n } _ { 2 } = 25$; two-tailed test, $\alpha = 0.10$  
A)Test statistic: $\mathrm { F } = 1.17$. Critical values $= 0.515,1.94$. Reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 1.36$. Critical values $= 0.515,1.94$. Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 1.17$. Critical values $= 0.529,1.94$. Do not reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 1.36$. Critical values $= 0.529,1.94$. Do not reject $\mathrm { H } _ { 0 }$.

Quizplus · Accepted Answer

The correct test statistic F is calculated by squaring the ratio of the two sample standard deviations, $(5.85/5.01)^2 \approx 1.36$. The critical values for a two-tailed test with $\alpha = 0.10$ and degrees of freedom corresponding to $n_1 - 1 = 30$ and $n_2 - 1 = 24$ should be looked up in an F-distribution table, which typically requires interpolation. The provided critical values $0.529$ and $1.94$ are plausible for such a test. Since the test statistic $1.36$ falls between the critical values, we do not reject the null hypothesis $H_0$, indicating no significant difference in variances at the 0.10 significance level.

The Sample Standard Deviations and Sample Sizes Are Given for Independent