Question

Three randomly selected households are surveyed. The numbers of people in the households are 1, 4 and 10. Assume that the samples of size n=2 are randomly selected with replacement from the population of 1, 4 and 10. Listed below are the nine different samples:
1,1 1,4 1,10 4,1 4,4 4,10 10,1 10,4 10,10

Find the variance of each of the nine samples: (find s^2 and probability)

s^2 is 4.5, 0, or 1? Whats the probability?
s^2 is 9, 4.5, 2.3? Whats the probability?
s^2 is 18, 72, or 9? Whats the probability?
s^2 is 20.3, 81 or 40.5? Whats the probability?

Compare the population variance to the mean of the sample variances. Choose the correct answer below:

A. The population variance is equal to the mean of the sample variance.
B. The population variance is equal to the square of the mean of the sample variances.
C. The population variance is equal to the square root of the mean of the sample variances.

Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or Why not?

A. The sample variances do not target the population variance, therefore, sample variances make good estimators of population variances.
B. The sample variances do not target the population variance, therefore, sample variances do not make good estimators of population variances.
C. The sample variances target the population variance, therefore, sample variances do not make good estimators of population variances.
D. The sample variances target the population variance, therefore, sample variances make good estimators of population variances.

Answer 1

If you submit each question separately, I think you'll get way more help.

Answer 2

Well those questions all work together... :-/

Answer 3

Try tagging people, you might get quicker help that way.