Question

The assets of four wealthiest people in a particular country are 29, 27, 14, 10. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values.

After Identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean, In the table, values of the sample mean that are the same have been combined.

x               Probability

29

28

27

21.5

20.5

19.5

18.5

14

12

10

b.) Compare the mean of the population to the mean of sampling distribution of the sample mean

C.) Do the sample means target the value of the population mean?

Answer 1

a)

sample			sample
mean	probability		mean	probability
29	1/16		19.5	1/8
28	1/8		18.5	1/8
27	1/16		14	1/16
21.5	1/8		12	1/8
20.5	1/8		10	1/16

b)

The mean of the​ population ,20 equal to the mean of the sample means 20

c)

The sample means target the population mean. In​ general, sample means do make good estimates of population means because the mean is an unbaised estimator