Assume a population of

1,

2,

and

12.

Assume that samples of size

n=2

are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below.

1,1

1,2

1,12

2,1

2,2

2,12

12,1

12,2

12,12

Question content area bottom

Part 1

a. Find the value of the population standard deviation

.

=enter your response here

(Round to three decimal places as needed.)

Part 2

b. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution of the distinct standard deviation values. Use ascending order of the sample standard deviations.

s	Probability
	0.5 0 1	enter your response here
	0.707 1 5	enter your response here
	50 10 7.071	enter your response here
	60.5 7.778 11	enter your response here

(Type integers or fractions.)

Part 3

c. Find the mean of the sampling distribution of the sample standard deviations.

The mean of the sampling distribution of the sample standard deviations is

enter your response here.

(Round to three decimal places as needed.)

d. Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

A.

The sample standard deviations do target the population standard deviation, therefore, sample standard deviations are biased estimators.

B.

The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are biased estimators.

C.

The sample standard deviations do target the population standard deviation, therefore, sample standard deviations are unbiased estimators.

D.

The sample standard deviations do not target the population standard deviation, therefore, sample standard deviations are unbiased estimators.