Question

Which of the following is NOT an advantage of pooling sample​ variances? Choose the correct answer below. A. We often know that sigma1equalssigma2. B. Confidence intervals are a little narrower. C. Hypothesis tests have more power. D. The number of degrees of freedom is a little higher.

Answer 1

Option A - we often know that
`\sigma_1=\sigma_2`

Explanation:

To find : Which of the following is NOT an advantage of pooling sample​ variances?

Solution :

Pooled variance is defined as a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.

So,

The sampling variance is pooled when there is assumption that the population variance are equal which is not an advantage.

i.e. we often know that
`\sigma_1=\sigma_2`

Therefore, option A is correct.

Answer 2

(a) we often know that
`\sigma _1=\sigma _2`

Explanation:

The sampling variance is pooled when there is assumption that the population variance are equal which is not an advantage. So
`\sigma _1=\sigma _2` will have no advantage of pooling sample variances
`\sigma _1=\sigma _2` is given in option (A) so option (A) will be the right answer