Consider a study in which the population variance estimate based on a treatment group of 14 participants is 8, and the population variance estimate based on a control group of 17 individuals is 9. Compute the pooled estimate of population variance.
A)8.55
B)9.22
C)10. 05
D)11.11

Question

Quizplus · Accepted Answer

The pooled estimate of population variance is calculated using the formula: $$s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}$$ where $n_1$ and $n_2$ are the sample sizes of the two groups, and $s_1^2$ and $s_2^2$ are the variances of the two groups. Plugging in the given values: $$s_p^2 = \frac{(14-1)*8 + (17-1)*9}{14 + 17 - 2} = \frac{13*8 + 16*9}{29} = \frac{104 + 144}{29} = \frac{248}{29} = 8.55.$$

Consider a Study in Which the Population Variance Estimate Based