Question

Assume a population of 1,2 and 12. assume the sample size of size n = 2 are randomly selected with replacement from the population. listed below are the nine different sample. complete parts a through d below

1,1 1,2 1,12, 2,1 2,2 2,12 12,1 12,2 12,12

a) find the value of the population standard deviation

b) find the standard deviation of each of the nine samples the summarize the sampling distribution of the standard deviation in the format of a table representing the probability distribution of the distinct standard deviation values. use ascending order

c) find the mean of the sampling distribution of the sample standard deviation

d) does the sample standard deviation target the value of the population?

Answer 1

We use Excel to solve this question.

We use Excel commands STDEV.S to find sample standard deviation and STDEV.P to find population standard deviation and then use AVERAGE command to find mean of the standard deviation of each 9 samples.

a) value of the population standard deviation = 4.97

Samp Std	Probability
0	0
0	0
0	0
0.71	0.02
0.71	0.02
7.07	0.23
7.07	0.23
7.78	0.25
7.78	0.25
Sum	1

c)

The mean of the sampling distribution of the sample standard deviation = 6.22

d)

The mean of the sampling distribution of the sample standard deviation = 6.22 and population standard deviation = 4.97

This implies sample standard deviation doesnot target the value of the population.

Sample No	Sample 1	Sample 2	Samp Std	Probability
1	1	1	0.00	0.00
2	1	2	0.71	0.02
3	1	12	7.78	0.25
4	2	1	0.71	0.02
5	2	2	0.00	0.00
6	2	12	7.07	0.23
7	12	1	7.78	0.25
8	12	2	7.07	0.23
9	12	12	0.00	0.00
		Sum	31.11	1.00
	Pop Std	4.97
		Mean	6.22