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.
-$\mathrm { s } _ { 1 } = 5.17 , \mathrm { n } _ { 1 } = 25 , \mathrm {~s} _ { 2 } = 2.35 , \mathrm { n } _ { 2 } = 17$; right-tailed test, $\alpha = 0.01$
A) Test statistic: $\mathrm { F } = 2.2 .$ Critical value $= 3.18 .$ Do not reject $\mathrm { H } _ { 0 } .$
B) Test statistic: $\mathrm { F } = 4.84 .$ Critical value: $\mathrm { F } = 3.18 .$ Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 4.84 .$ Critical value: $\mathrm { F } = 3.18 .$ Reject $\mathrm { H } _ { 0 } .$
D) Test statistic: $\mathrm { F } = 2.2$. Critical value $= 1.87 .$ 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.
-$\mathrm { s } _ { 1 } = 5.17 , \mathrm { n } _ { 1 } = 25 , \mathrm {~s} _ { 2 } = 2.35 , \mathrm { n } _ { 2 } = 17$; right-tailed test, $\alpha = 0.01$  
A) Test statistic: $\mathrm { F } = 2.2 .$ Critical value $= 3.18 .$ Do not reject $\mathrm { H } _ { 0 } .$
B) Test statistic: $\mathrm { F } = 4.84 .$ Critical value: $\mathrm { F } = 3.18 .$ Do not reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $\mathrm { F } = 4.84 .$ Critical value: $\mathrm { F } = 3.18 .$ Reject $\mathrm { H } _ { 0 } .$
D) Test statistic: $\mathrm { F } = 2.2$. Critical value $= 1.87 .$ Reject $\mathrm { H } _ { 0 } .$

Quizplus · Accepted Answer

The test statistic F is calculated by squaring the ratio of the two standard deviations ($F = (s_1 / s_2)^2$). Here, $F = (5.17 / 2.35)^2 = 4.84$. For a right-tailed test with $\alpha = 0.01$, and degrees of freedom $df_1 = 24$ and $df_2 = 16$, the critical value is approximately 3.18. Since the test statistic $F = 4.84$ is greater than the critical value $3.18$, we reject $H_0$.

The Sample Standard Deviations and Sample Sizes Are Given for Independent