Question

When testing the difference between two independent population means, the sample variances are pooled to estimate the population variance when ________. Multiple Choice the population means are known the population variances are assumed equal but unknown the population variances are assumed unequal and unknown the population variances are known and equal

Answer 1

the population means are known the population variances are assumed equal but unknown

Explanation:

If σ1= σ2 (= σ) but unknown , then the biased pooled or combined estimate of the common variance σ² ( the term common variance means that each population has the same variance ) is given by

Sp²= (n1-1) s1² + (n2-1) s2²/ n1+ n2- 2

So first assumption is correct.

When the population variances are assumed unequal and unknown

If σ1 ≠ σ2 but unknown

we use the sample estimates s1 and s2 to compute the standard error of the difference between the means.

S(x1`- x2`) = √s1²/ n1 + s2²/n2

So this is does not apply here.