Question

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 37, 33, 23 ,15.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.

x probability x probability

37 26

35 24

33 23

30 19

28 15

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

The mean of the​ population----- is ------▼ 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-------- the population mean. In general sample means ------- make good estimates of population means because the mean is -------- estimator

▼

target

do not target

the population mean. In​ general, sample means

▼

do not

do

make good estimates of population means because the mean is

▼

an unbiased

a biased

estimator.

Answer 1

below is sampling distribution of mean:

x1	x2	probabilityP(x1,x2)		x̅
37	37	0.0625		37
37	33	0.0625		35
37	23	0.0625		30
37	15	0.0625		26
33	37	0.0625		35
33	33	0.0625		33
33	23	0.0625		28
33	15	0.0625		24
23	37	0.0625		30
23	33	0.0625		28
23	23	0.0625		23
23	15	0.0625		19
15	37	0.0625		26
15	33	0.0625		24
15	23	0.0625		19
15	15	0.0625		15

a)

sample			sample
mean	probability		mean	probability
37	1/16		26	1/8
35	1/8		24	1/8
33	1/16		23	1/16
30	1/8		19	1/8
28	1/8		15	1/16

b)

The mean of the​ population ,27 equal to the mean of the sample means 27

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