Test the hypothesis that $\sigma _ { 1 } \sigma _ { 2 } \text { at the } \alpha = 0.01$ level of significance for the given sample data. $\begin{array} { c | c c } & \text { Population 1 } & \text { Population 2 } \ \hline \mathrm { n } & 61 & 31 \ \mathrm {~s} & 34.4 & 27.6 \end{array}$ A) Test statistic: F=1.55 . Critical value =2.21 . Do not reject H₀ B) Test statistic: F=1.55 . Critical value =2.03 . Reject H₀ C) Test statistic: F=42.88 . Critical value =2.03 . Reject H₀ D) Test statistic: F=1.25 . Critical value =2.21 . 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. $\begin{array} { c | c c } & \text { Population 1 } & \text { Population 2 } \ \hline \mathrm { n } & 61 & 31 \ \mathrm {~s} & 34.4 & 27.6 \end{array}$ A) Test statistic: F=1.55 . Critical value =2.21 . Do not reject H₀ B) Test statistic: F=1.55 . Critical value =2.03 . Reject H₀ C) Test statistic: F=42.88 . Critical value =2.03 . Reject H₀ D) Test statistic: F=1.25 . Critical value =2.21 . Do not reject H₀

Quizplus · Accepted Answer

The correct test statistic for comparing two variances (or standard deviations) is the F-test. The F-value is calculated by dividing the larger variance by the smaller variance. Here, $F = \frac{34.4^2}{27.6^2} = 1.55$. The critical value for an F-test at the $\alpha = 0.01$ level of significance with degrees of freedom $df_1 = 60$ (for population 1) and $df_2 = 30$ (for population 2) is closer to the value given in option A, which indicates not rejecting the null hypothesis. Options B and C provide incorrect interpretations or calculations, and D has an incorrect F-value calculation.

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