Question

Assume that the 129 patients in the Patients dataset (Excel) represent the entire population of interest. If you were interested in age of the patients and took a sample of 25 patients from this population, what is the standard error of the mean?   What if you took a sample 64 patients from this population, what is the standard error of the mean? What happens to the standard error of the mean as the sample size increases? Why does that make logical sense?

Mean 75

Standard Deviation 12.097988

Age (Years)
78
74
89
81
87
65
90
61
90
78
78
71
76
76
79
72
72
64
72
69
63
78
83
62
71
83
63
83
76
79
65
79
74
63
84
90
73
81
75
87
70
73
77
71
76
49
78
86
67
69
73
88
67
69
77
64
76
64
41
49
59
81
74
77
78
73
67
80
77
73
67
86
82
84
73
82
62
84
89
84
81
81
78
84
37
62
80
80
73
80
80
80
81
39
86
79
87
53
83
80
79
72
77
81
67
80
67
88
88
92
85
85
80
98
74
77
53
93
83
80
79
87
59
81
94
33
78
29
80

Answer 1

Solution :

There are 129 patients in the Patients dataset (Excel) that represent the entire population of interest. The formula for calculating the Standard Error of Mean is given as ,

The Sample Mean for the dataset is ,

The Sample Standard Deviation for the dataset is ,

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The Standard Error of Mean for a sample of 25 patients is given as ,

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The Standard Error of Mean for a sample of 64 patients is given as ,

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We can clearly see that the Standard Error of the Mean decreases from 2.419598 to 1.512249 as the Sample Size increases from 25 to 64..... That is ,   .

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We know that the formula for calculating the Standard Error of Mean is given as ,

Now , clearly , when the Sample Size becomes very large , the SE becomes very small. That is ,

Thus , it makes a logical sense that as Sample Size (n) increases , the Standard Error of the Mean (SE) decreases !!

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