In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal,the degrees of freedom is: A) n₁ + n₂ B) n₁ + n₂ - 2 C) n₁ + n₂ - 1 D) None of these choices

Question

Quizplus · Accepted Answer

The formula for the degrees of freedom in this situation is given by (n1-1) + (n2-1) = n1 + n2 - 2. However, in the case where the variances are unknown but assumed equal, we use a pooled variance estimate, given by (n1-1)S1^2 + (n2-1)S2^2 / (n1+n2-2). This estimate reduces the degrees of freedom, so we need to adjust our formula accordingly. The final formula is (n1+n2-2) * [S1^2/(n1-1) + S2^2/(n2-1)] / [S1^2/(n1-1) + S2^2/(n2-1)]^2 = (n1+n2-2) * [S1^2S2^2 / ((n1-1)(n2-1))] / [(S1^2/(n1-1)) + (S2^2/(n2-1))] = (n1+n2-2) * [((n1-1)(n2-1))/((n1+n2-2))] = n1+n2-2 + F1-F10, where F1-F10 is the F-distribution value at a certain level of significance. Therefore, the correct choice is B.

In Testing for the Differences Between the Means of Two