The test statistic employed to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1 \text { is } F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$
,which is F distributed with $n _ { 1 } - 1 \text { and } n _ { 2 } - 1$
degrees of freedom.

Question

The test statistic employed to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1 \text { is } F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$ 
,which is F distributed with $n _ { 1 } - 1 \text { and } n _ { 2 } - 1$ 
degrees of freedom.

Quizplus · Accepted Answer

The F-test is used to compare two variances, and the test statistic $ F = \frac{s_1^2}{s_2^2} $ follows an F-distribution with $ n_1 - 1 $ and $ n_2 - 1 $ degrees of freedom, where $ s_1^2 $ and $ s_2^2 $ are the sample variances.

The Test Statistic Employed to Test H0:σ12/σ22=1 is F=s12/s22H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1 \text { is } F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }H0​:σ12​/σ22​=1 is F=s12​/s22​

The Test Statistic Employed to Test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1 \text { is } F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$