A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows.
-What is the pooled estimate of the population variance?
A)[(14 / 36)(6.5)] + [(22 / 36)(4.5)] = 5.28
B)[(15 / 38)(6.5)] + [(23 / 38)(4.5)] = 5.29
C)[(15 / 23)(6.5)] + [(23 / 15)(4.5)] = 11.14
D)[(14 / 22)(6.5)] + [(22 / 14)(4.5)] = 11.21

Question

A social psychologist interested in cultural differences compared women of two ethnic groups on a Role Approval Index on which high scores indicated high degrees of approval of one's own social role. The results were as follows. 
-What is the pooled estimate of the population variance?
A)[(14 / 36)(6.5)] + [(22 / 36)(4.5)] = 5.28 
B)[(15 / 38)(6.5)] + [(23 / 38)(4.5)] = 5.29 
C)[(15 / 23)(6.5)] + [(23 / 15)(4.5)] = 11.14 
D)[(14 / 22)(6.5)] + [(22 / 14)(4.5)] = 11.21

Quizplus · Accepted Answer

The pooled estimate of the population variance is calculated by taking a weighted average of the variances of two or more groups, with the weights being proportional to the degrees of freedom (or sample sizes minus one) of each group. The formula for the pooled variance when combining two groups is: $$s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}$$ where $n_1$ and $n_2$ are the sample sizes of the two groups, and $s_1^2$ and $s_2^2$ are their variances, respectively. The correct calculation must correctly apply the weights based on the sample sizes or degrees of freedom of each group. Choice A correctly applies the formula for pooled variance, using the given sample sizes and variances, and thus provides the correct pooled estimate of the population variance.

A Social Psychologist Interested in Cultural Differences Compared Women of Two