Respuesta :
Answer:
[tex] s^2 = \frac{SS}{n-1}[/tex]
And if we take the average value of the sample variances from all the possible random samples we will get the population variance:
[tex]\sigma =\frac{SS}{n}[/tex]
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:
[tex] SS = \sum_{i=1}^n (X_i -\bar X)^2[/tex]
Where:
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
And we can find the sample variance with this formula:
[tex] s^2 = \frac{SS}{n-1}[/tex]
And if we take the average value of the sample variances from all the possible random samples we will get the population variance:
[tex]\sigma =\frac{SS}{n}[/tex]
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
