When the necessary conditions are met, a two-tail test is being conducted at $\alpha$ = 0.05 to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1$ . The two sample variances are $s _ { 1 } ^ { 2 } = 500 \text { and } s _ { 2 } ^ { 2 } = 900$ , and the sample sizes are $n _ { 1 } = 21 \text { and } n _ { 2 } = 31$ . The rejection region is F 2.20 or F

Question

When the necessary conditions are met, a two-tail test is being conducted at $\alpha$ = 0.05 to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1$ . The two sample variances are $s _ { 1 } ^ { 2 } = 500 \text { and } s _ { 2 } ^ { 2 } = 900$ , and the sample sizes are $n _ { 1 } = 21 \text { and } n _ { 2 } = 31$ . The rejection region is F > 2.20 or F < 0.4255.

Quizplus · Accepted Answer

The F-statistic is calculated as $ F = \frac{s_1^2}{s_2^2} = \frac{500}{900} = 0.5556 $. Since 0.5556 is not greater than 2.20 or less than 0.4255, the null hypothesis is not rejected.

When the Necessary Conditions Are Met, a Two-Tail Test Is α\alphaα

When the Necessary Conditions Are Met, a Two-Tail Test Is $\alpha$