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.
-$\mathrm { s } _ { 1 } = 32.2 , \mathrm { n } _ { 1 } = 61 , \mathrm {~s} _ { 2 } = 26.8 , \mathrm { n } _ { 2 } = 31 \text {; right-tailed test, } \alpha = 0.01$
A)Test statistic: $\mathrm { F } = 38.69$. Critical value $= 2.03$. Reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $\mathrm { F } = 1.44$. Critical value $= 2.21$. Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 1.44$. Critical value $= 2.03$. Reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $\mathrm { F } = 1.2$. Critical value $= 2.21$. Do not reject $\mathrm { H } _ { 0 }$.

Question

Quizplus · Accepted Answer

The test statistic for an F-test comparing two variances is calculated as the ratio of the larger sample variance to the smaller sample variance. Here, $F = \frac{s_1^2}{s_2^2} = \frac{32.2^2}{26.8^2} = 1.44$. The critical value for a right-tailed test with $\alpha = 0.01$ and degrees of freedom $df_1 = 60$ and $df_2 = 30$ (approximated because exact values depend on F-distribution tables) would be around 2.21, not 2.03. Therefore, since the test statistic is less than the critical value, we do not reject the null hypothesis.

The Sample Standard Deviations and Sample Sizes Are Given for Independent