When comparing the variances of two normally distributed populations using independent random samples,if $s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }$
the calculated value of F will always be equal to one.

Question

When comparing the variances of two normally distributed populations using independent random samples,if $s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }$ 
the calculated value of F will always be equal to one.

Quizplus · Accepted Answer

When the variances of both populations are equal and the samples are independent and randomly drawn, the calculated value of F will always be equal to 1. This is the null hypothesis in the F-test for equal variances.

When Comparing the Variances of Two Normally Distributed Populations Using s12=s22s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }s12​=s22​

When Comparing the Variances of Two Normally Distributed Populations Using $s _ { 1 } ^ { 2 } = s _ { 2 } ^ { 2 }$