Question

If sample variance is computed by dividing SS by df = n – 1, then the average value of the sample variances from all the possible random samples will be ____ the population variance

Answer 1

Answer:

$s^2 = \frac{SS}{n-1}$

And if we take the average value of the sample variances from all the possible random samples we will get the population variance:

$\sigma =\frac{SS}{n}$

So then the best answer for this case would be:

The average value of the sample variances from all the possible random samples will be exactly the population variance

Step-by-step explanation:

For this case we can define the sum of squares with this formula:

$SS = \sum_{i=1}^n (X_i -\bar X)^2$

Where:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

And we can find the sample variance with this formula:

$s^2 = \frac{SS}{n-1}$

And if we take the average value of the sample variances from all the possible random samples we will get the population variance:

$\sigma =\frac{SS}{n}$

So then the best answer for this case would be:

The average value of the sample variances from all the possible random samples will be exactly the population variance