Question

a.) Write down all feasible samples of size 2 of the values in the following table and calculate the average number of cases in each. (Hint: There are 45 possible combinations of size 2.)
b.) Compare the average value of the distribution of sample means with that of the population. Write what you observe.
c.) In a graph compare the dispersion of the population with that of the sample means. Write what you observe.

Validity	Zone A
01/01/2019	$102.68
01/01/2018	$88.36
01/01/2017	$80.04
01/01/2016	$73.04
01/01/2015	$70.10
01/01/2014	$67.29
01/01/2013	$64.76
01/01/2012	$62.33
01/01/2011	$59.82
01/01/2010	$57.46

Answer 1

a)

All the 45 possible combinations of size 2 are shown below . The average is obtained in excel using the function =AVERAGE() and the standard deviation is obtained using the function =STDEV().

Sample	1	2	Average
1	102.68	88.36	95.52
2	102.68	80.04	91.36
3	102.68	73.04	87.86
4	102.68	70.10	86.39
5	102.68	67.29	84.99
6	102.68	64.76	83.72
7	102.68	62.33	82.51
8	102.68	59.82	81.25
9	102.68	57.46	80.07
10	88.36	80.04	84.20
11	88.36	73.04	80.70
12	88.36	70.10	79.23
13	88.36	67.29	77.83
14	88.36	64.76	76.56
15	88.36	62.33	75.35
16	88.36	59.82	74.09
17	88.36	57.46	72.91
18	80.04	73.04	76.54
19	80.04	70.10	75.07
20	80.04	67.29	73.67
21	80.04	64.76	72.40
22	80.04	62.33	71.19
23	80.04	59.82	69.93
24	80.04	57.46	68.75
25	73.04	70.10	71.57
26	73.04	67.29	70.17
27	73.04	64.76	68.90
28	73.04	62.33	67.69
29	73.04	59.82	66.43
30	73.04	57.46	65.25
31	70.10	67.29	68.70
32	70.10	64.76	67.43
33	70.10	62.33	66.22
34	70.10	59.82	64.96
35	70.10	57.46	63.78
36	67.29	64.76	66.03
37	67.29	62.33	64.81
38	67.29	59.82	63.56
39	67.29	57.46	62.38
40	64.76	62.33	63.55
41	64.76	59.82	62.29
42	64.76	57.46	61.11
43	62.33	59.82	61.08
44	62.33	57.46	59.90
45	59.82	57.46	58.64
Average			72.59
Std.Dev			9.05

b.)

similarly for the population, the average is obtained in excel using the function =AVERAGE() and the standard deviation is obtained using the function =STDEV().

Validity	Zone A
01-01-2019	102.68
01-01-2018	88.36
01-01-2017	80.04
01-01-2016	73.04
01-01-2015	70.10
01-01-2014	67.29
01-01-2013	64.76
01-01-2012	62.33
01-01-2011	59.82
01-01-2010	57.46
Average	72.59
SD	14.15259

We can observe that the mean for the population and all the possible sample is same.

	mean
Population	72.59
Sample	72.59

c.)

The normal probability plot can be obtained in any online applet. Here i make the plot in Statkey by following these steps,

For population

Step 1: Open StatKey in browser > Theoretical Distribution > Normal. The screenshot is shown below,

Step 2: Click Edit Parameter > enter Mean = 72.59 and Standard Deviation = 14.15259 > OK. The screenshot is shown below,

The normal probability plot is obtained. The screenshot is shown below,

For sample

Step 1: Same

Step 2: Click Edit Parameter > enter Mean = 72.59 and Standard Deviation = 9.05 > OK. The screenshot for the plot is shown below,

Conclusion: From both the plot we can observe that the sample has smaller variance compare to population.