Test the hypothesis that $\sigma _ { 1 }

Question

Test the hypothesis that $\sigma _ { 1 } < \sigma _ { 2 } \text { at the } \alpha = 0.05$ level of significance for the given sample data. $\begin{array} { c | c c } & \text { Population 1 } & \text { Population 2 } \ \hline \mathrm { n } & 9 & 10 \ \mathrm {~s} & 0.0782 & 0.1955 \end{array}$ A) Test statistic: F=0.16 Critical value: 0.295 . Reject H₀ B) Test statistic: F=0.16 Critical value: 0.310 . Reject H₀ C) Test statistic: F=0.16 Critical value: 0.318 . Do not reject H₀ D) Test statistic: F=0.16 Critical value: 0.295 . Do not reject H₀

Quizplus · Accepted Answer

The test statistic is calculated as F = (s1^2 / s2^2) = (0.0782^2 / 0.1955^2) = 0.16. The critical value for a one-tailed test at the 0.05 level of significance with 8 and 9 degrees of freedom is 0.295. Since the test statistic (0.16) is less than the critical value (0.295), we reject the null hypothesis and conclude that σ1 < σ2.

Test the Hypothesis That σ1<σ2 at the α=0.05\sigma _ { 1 } < \sigma _ { 2 } \text { at the } \alpha = 0.05σ1​<σ2​ at the α=0.05

Test the Hypothesis That $\sigma _ { 1 } < \sigma _ { 2 } \text { at the } \alpha = 0.05$