In testing for the equality of two population variances, when the populations are normally distributed, the 5% level of significance has been used. To determine the rejection region, it will be necessary to refer to the F table corresponding to an upper-tail area of:
A) 0.950.
B) 0.050.
C) 0.025.
D) 0.100.

Question

Quizplus · Accepted Answer

When testing for the equality of two population variances using the F-test, we calculate the test statistic F as the ratio of the sample variances:
F = s1^2 / s2^2

Under the null hypothesis of equal variances, this test statistic follows an F-distribution with degrees of freedom (df1 = n1 - 1) and (df2 = n2 - 1).

To determine the rejection region at the 5% level of significance, we need to find the critical value of F from the F distribution table with df1 and df2 degrees of freedom at the upper-tail area of 0.05.

Looking at the F distribution table, we can see that the critical value of F for an upper-tail area of 0.05 and df1 = df2 = (n1 - 1) = (n2 - 1) is 2.16.

Therefore, the rejection region for the F-test at the 5% level of significance is F > 2.16.

In Testing for the Equality of Two Population Variances, When