Question

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 42, 35, 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.

42

38.5

36.5

35

33

31

30

26.5

24.5

18

b. Compare the mean of the population to the mean of the sampling distribution of the sample mean. The mean of the​ population, nothing​, is ▼ (less than) (greater than) (equal to) the mean of the sample​ means, _______. ​(Round to two decimal places as​ needed.)

c. Do the sample means target the value of the population​ mean? In​ general, do sample means make good estimates of population​ means? Why or why​ not? The sample means ▼ (do not target) (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

below is sampling distribution of xbar:

x1	x2	probabilityP(x1,x2)		x̅
42	42	1/16		42
42	35	1/16		38.5
42	31	1/16		36.5
42	18	1/16		30
35	42	1/16		38.5
35	35	1/16		35
35	31	1/16		33
35	18	1/16		26.5
31	42	1/16		36.5
31	35	1/16		33
31	31	1/16		31
31	18	1/16		24.5
18	42	1/16		30
18	35	1/16		26.5
18	31	1/16		24.5
18	18	1/16		18

a)

sample			sample
mean	probability		mean	probability
42	1/16		31	1/16
38.5	1/8		30	1/8
36.5	1/8		26.5	1/8
35	1/16		24.5	1/8
33	1/8		18	1/16

b)

The mean of the​ population 31.5 equal to the mean of the sample means 31.5

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