Question

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 33, 30, 19, 12.

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.

Xbar	Probability		Xbar	Probability
33			22.5
31.5			21
30			19
26			15.5
24.5			12

​

Answer 1

a)

below is sampling distribution of sample mean :

x1	x2	probabilityP(x1,x2)		x̅
33	33	1/16		33
33	30	1/16		31.5
33	19	1/16		26
33	12	1/16		22.5
30	33	1/16		31.5
30	30	1/16		30
30	19	1/16		24.5
30	12	1/16		21
19	33	1/16		26
19	30	1/16		24.5
19	19	1/16		19
19	12	1/16		15.5
12	33	1/16		22.5
12	30	1/16		21
12	19	1/16		15.5
12	12	1/16		12

sample			sample
mean	probability		mean	probability
33	1/16		22.5	1/8
31.5	1/8		21	1/8
30	1/16		19	1/16
26	1/8		15.5	1/8
24.5	1/8		12	1/16