Test the hypothesis that $\sigma _ { 1 } \sigma _ { 2 } \text { at the } \alpha = 0.01$ level of significance for the given sample data. $\begin{array} { c | c c } & \text { Population 1 } & \text { Population 2 } \ \hline \mathrm { n } & 25 & 17 \ \mathrm {~s} & 5.23 & 2.5 \end{array}$ A) Test statistic: F=4.38 . Critical value: \mathrm{F}=3.18 . Reject H₀ B) Test statistic: F=4.38 . Critical value: \mathrm{F}=3.18 . Do not reject H₀ C) Test statistic: F=2.09 . Critical value =1.87 . Reject H₀ D) Test statistic: F=2.09 . Critical value =3.18 . Do not reject H₀

Question

Test the hypothesis that $\sigma _ { 1 } > \sigma _ { 2 } \text { at the } \alpha = 0.01$ level of significance for the given sample data. $\begin{array} { c | c c } & \text { Population 1 } & \text { Population 2 } \ \hline \mathrm { n } & 25 & 17 \ \mathrm {~s} & 5.23 & 2.5 \end{array}$ A) Test statistic: F=4.38 . Critical value: \mathrm{F}=3.18 . Reject H₀ B) Test statistic: F=4.38 . Critical value: \mathrm{F}=3.18 . Do not reject H₀ C) Test statistic: F=2.09 . Critical value =1.87 . Reject H₀ D) Test statistic: F=2.09 . Critical value =3.18 . Do not reject H₀

Quizplus · Accepted Answer

The test statistic for comparing two variances using an F-test is calculated as $F = \frac{s_1^2}{s_2^2}$, where $s_1^2$ and $s_2^2$ are the sample variances of the two populations. Here, $F = \frac{5.23^2}{2.5^2} = 4.38$. The critical value for an F-test at the $\alpha = 0.01$ level of significance with degrees of freedom $df_1 = n_1 - 1 = 24$ and $df_2 = n_2 - 1 = 16$ is approximately 3.18. Since the test statistic (4.38) is greater than the critical value (3.18), we reject the null hypothesis, indicating that there is significant evidence at the 0.01 level to conclude that $\sigma_1 > \sigma_2$.

Test the Hypothesis That σ1>σ2 at the α=0.01\sigma _ { 1 } > \sigma _ { 2 } \text { at the } \alpha = 0.01σ1​>σ2​ at the α=0.01

Test the Hypothesis That $\sigma _ { 1 } > \sigma _ { 2 } \text { at the } \alpha = 0.01$