Three randomly selected households are surveyed. The numbers of people in the ho

Question

Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 9. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 9. Listed below are the nine different samples. Complete parts (a) through (c).
2,2
2,4
2,9
4,2
4,4
4,9
9,2
9,4
9,9

a) Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values. Type a fraction; use ascending order of sample variances.

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

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

s2 Probability ? ? ? ? ? ? ? ?

Explanation / Answer

as each sample has equal probability ; terefore probability of each sample =1/9

therefore from above:

b)  A. The population variance is equal to the mean of the sample variances.

c)

A. The sample variances target the population variances, therefore, sample variances make good estimators of population variances.

s2 probability 0 1/3 2 2/9 12.5 2/9 24.5 2/9

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