Military Presidents – Here is the population of all five U.S. presidents who had
ID: 3362936 • Letter: M
Question
Military Presidents – Here is the population of all five U.S. presidents who had professions in the military, along with their ages at inauguration: Eisenhower (62), Grant (46), Harrison (68), Taylor (64), and Washington (57). Assume that samples of size 2 are randomly selected with replacement from the population of five ages. This exercise can be done in Excel as per instructions . After completing this Exercise in Excel . .
a. Sampling Distribution of the Mean.
1). Find the mean of each of the 25 samples, then find the mean of the sample means.
2). Find the mean of the population.
3). Compare the population mean to the mean of the sample means. Do the sample means target the value of the population mean? In general, do the sample means make a good estimator of the population mean? Is the Mean a biased or unbiased estimator?
Explanation / Answer
Result:
Sample #
Num1
Num2
Mean
Median
Variance
Stdev
1
62
46
54
54
11.3137
3.3636
2
46
68
57
57
15.5563
3.9442
3
68
64
66
66
2.8284
1.6818
4
64
57
60.5
60.5
4.9497
2.2248
5
57
62
59.5
59.5
3.5355
1.8803
6
68
46
57
57
15.5563
3.9442
7
64
68
66
66
2.8284
1.6818
8
57
64
60.5
60.5
4.9497
2.2248
9
62
57
59.5
59.5
3.5355
1.8803
10
46
62
54
54
11.3137
3.3636
11
68
46
57
57
15.5563
3.9442
12
62
68
65
65
4.2426
2.0598
13
46
64
55
55
12.7279
3.5676
14
68
57
62.5
62.5
7.7782
2.7889
15
64
68
66
66
2.8284
1.6818
16
57
64
60.5
60.5
4.9497
2.2248
17
68
57
62.5
62.5
7.7782
2.7889
18
64
62
63
63
1.4142
1.1892
19
57
46
51.5
51.5
7.7782
2.7889
20
62
68
65
65
4.2426
2.0598
21
46
57
51.5
51.5
7.7782
2.7889
22
68
68
68
68
0.0000
0.0000
23
57
64
60.5
60.5
4.9497
2.2248
24
62
57
59.5
59.5
3.5355
1.8803
25
46
64
55
55
12.7279
3.5676
Avg
59.86
Mean of the sample means =59.86
Mean = 59.4
3). Compare the population mean to the mean of the sample means. Do the sample means target the value of the population mean? In general, do the sample means make a good estimator of the population mean? Is the Mean a biased or unbiased estimator?
Mean of the sample means is near to the Population mean . Sample means target the value of the population mean. sample means makes a good estimator of the population mean. Mean is a unbiased estimator.
Sample #
Num1
Num2
Mean
Median
Variance
Stdev
1
62
46
54
54
11.3137
3.3636
2
46
68
57
57
15.5563
3.9442
3
68
64
66
66
2.8284
1.6818
4
64
57
60.5
60.5
4.9497
2.2248
5
57
62
59.5
59.5
3.5355
1.8803
6
68
46
57
57
15.5563
3.9442
7
64
68
66
66
2.8284
1.6818
8
57
64
60.5
60.5
4.9497
2.2248
9
62
57
59.5
59.5
3.5355
1.8803
10
46
62
54
54
11.3137
3.3636
11
68
46
57
57
15.5563
3.9442
12
62
68
65
65
4.2426
2.0598
13
46
64
55
55
12.7279
3.5676
14
68
57
62.5
62.5
7.7782
2.7889
15
64
68
66
66
2.8284
1.6818
16
57
64
60.5
60.5
4.9497
2.2248
17
68
57
62.5
62.5
7.7782
2.7889
18
64
62
63
63
1.4142
1.1892
19
57
46
51.5
51.5
7.7782
2.7889
20
62
68
65
65
4.2426
2.0598
21
46
57
51.5
51.5
7.7782
2.7889
22
68
68
68
68
0.0000
0.0000
23
57
64
60.5
60.5
4.9497
2.2248
24
62
57
59.5
59.5
3.5355
1.8803
25
46
64
55
55
12.7279
3.5676
Avg
59.86