Question

The assets (in billions of dollars) of the four wealthiest people in a particular country are 34, 33, 31, 18. Assume that samples of size n = 2 are randomly selected with replacement from this population of four values.

a. 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.

b. The mean of the population, ( ? ) , is (less than/equal to/greater than) the mean of the sample means, ( ? ).

c. The sample means (target/do not target) the population mean. In general, sample means (do not, do) make good estimates of population means because the mean is (a biased/an unbiased) estimator.

Answer 1

Sample 1	Sample 2	Mean
34	34	34
33	34	33.5
31	34	32.5
18	34	26
34	33	33.5
33	33	33
31	33	32
18	33	25.5
34	31	32.5
33	31	32
31	31	31
18	31	24.5
34	18	26
33	18	25.5
31	18	24.5
18	18	18

Mean of sample mean = 464/16 = 29

mean of population mean = ( 34 + 33 + 31 + 18 ) / 4 = 29

b. The mean of the population 29, is equal to the mean of the sample means 29.

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