Question

2. Three randomly selected households are surveyed. The numbers of people in the households are 1​, 4​, and 10. Assume that 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. Complete parts​ (a) through​ (c).

Sample            x1        x2

1          1          1

2          1          4

3          1          10

4          4          1

5          4          4

6          4          10

7          10        1

8          10        4

9          10        10

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

                                    S^2                                                                      Probability

(4.5, 0,1)
(2.3,4.5,9)
(72,9,18)
(40.5,81,20.3)

​(Type an integer or a fraction. Use ascending order of the 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 of the mean of the sample variances.

C. The population variance is equal to the square root 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 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​ variances, therefore, sample variances make good estimators of population variances.

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

Answer 1

Given Data

n=2

Excel Formulae

Sum : =Sum(x1,x2)

Mean: =average(x1,x2)

Median : =median(x1,x2)

variance =

                            S^2 (ascending order) Probability

(0,1,4.5)	0/9
(2.3,4.5,9)	2/9
(9,18,72)	2/9
(20.3,40.5,81)	2/9

​b)Compare the population variance to the mean of the sample variances

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

Hence option A is correct

c) The sample variances target the population​ variances, therefore, sample variances make good estimators of population variances.

Hence option C is correct