Question

The assets​ (in billions of​ dollars) of the four wealthiest people in a particular country are 43 comma 26 comma 17 comma 1343, 26, 17, 13. Assume that samples of size nequals=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 overbarx	Probability		x overbarx	Probability
4343	nothing		21.521.5	nothing
34.534.5	nothing		19.519.5	nothing
3030	nothing		1717	nothing
2828	nothing		1515	nothing
2626	nothing		1313	nothing

​(Type integers or​ fractions.)

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

equal to

greater than

the mean of the sample​ means,

nothing.

​(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

▼

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

the sample mean that are the same have been combined.

x overbarx	Probability		x overbarx	Probability
43	1 / 16		21.5	2 / 16
34.5	2 / 16		19.5	2 / 16
30	2 / 16		17	1 / 16
28	2 / 16		15	2 / 16
26	1 / 16		13	1 / 16

b )

The mean of the​ population, 24.75​, is equal to the mean of the sample​ means, 24.75.

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.