The quantity is called the pooled variance estimate of the common variance of two unknown but equal population variances.It is the weighted average of the two sample variances,where the weights represent the:
A) sample variances.
B) sample standard deviations.
C) degrees of freedom for each sample.
D) None of these choices.

Question

The quantity  is called the pooled variance estimate of the common variance of two unknown but equal population variances.It is the weighted average of the two sample variances,where the weights represent the:
A) sample variances. 
B) sample standard deviations. 
C) degrees of freedom for each sample. 
D) None of these choices.

Quizplus · Accepted Answer

The pooled variance estimate is calculated using the formula:

( (n1-1)s1^2 + (n2-1)s2^2 ) / (n1+n2-2)

where n1 and n2 are the sample sizes, s1^2 and s2^2 are the sample variances. The weights in this formula are the degrees of freedom for each sample (n1-1 and n2-1), which represent the number of independent observations in each sample that contribute to the estimate of the population variance. Therefore, the correct choice is C.

The Quantity Is Called the Pooled Variance Estimate of the Common