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

Question

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

Quizplus · Accepted Answer

The test statistic $F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$ is F-distributed with $v _ { 1 } = n _ { 1 } - 1$ and $v _ { 2 } = n _ { 2 } - 1$ degrees of freedom, provided that the two populations are normally distributed, not F-distributed.

The Test Statistic Employed to Test H0:σ12/σ22=1H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1H0​:σ12​/σ22​=1

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