Test the hypothesis that $\sigma _ { 1 } \neq \sigma _ { 2 } \text { at the } \alpha = 0.05$ level of significance for the given sample data. $\begin{array} { c | c c } & \text { Population 1 } & \text { Population 2 } \ \hline \mathrm { n } & 16 & 13 \ \mathrm {~s} & 20.7 & 22.9 \end{array}$ A) T́est statistic: F=0.82 . Critical values =0.338,3.18 . Do not reject H₀ B) Test statistic: F=0.82 . Critical values =0.314,3.18 . Do not reject H₀ C) Test statistic: F=0.82 . Critical values =0.338,3.18 . Reject H₀ D) Test statistic: F=0.82 . Critical values =0.403,2.62 . Reject H₀ .

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Quizplus · Accepted Answer

The test statistic $F$ is calculated as the ratio of the two sample variances $s_1^2 / s_2^2$, which equals $20.7^2 / 22.9^2 = 0.82$. The critical values for an $F$-test at the $\alpha = 0.05$ level of significance depend on the degrees of freedom for each sample, which are $n_1 - 1 = 15$ and $n_2 - 1 = 12$. The provided critical values $0.338$ and $3.18$ are consistent with typical $F$-distribution tables for these degrees of freedom. Since the test statistic $0.82$ falls between the critical values, we do not reject the null hypothesis that $\sigma_1 = \sigma_2$.

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

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