Question

TestScores
53
53
56
56
56
58
58
58
59
59
59
60
60
62
63
63
63
64
65
65
66
67
67
67
67
68
69
69
69
69
71
71
72
72
72
72
73
73
73
73
73
74
75
75
75
76
76
76
76
77
77
77
77
77
78
78
78
79
79
79
79
80
80
80
80
80
80
81
81
81
82
82
83
83
83
83
84
84
84
84
84
85
85
85
85
86
86
87
87
87
87
87
88
88
89
89
89
90
90
90
90
91
93
96

Confidence Interval: 95%

USE THESE NUMBERS AS THE RANDOM SAMPLE DATA: 82, 66, 91, 58, 53, 68, 72, 96, 56, 84

Take a random sample of 10 data values from column 1 “TestScore” Using the sample that you selected, determine and state the sample mean. Compare the sample mean to the original confidence interval. Is the sample of 10 data values you selected a “good sample”? Explain why!

Answer 1

From the data: = 75.67, s = 10.32

Since population standard deviation is unknown, the tcritical (2 tail) for = 0.05, for df = n -1 = 103, is 1.9833

The Confidence Interval is given by ME, where

ME = tcritical * \frac{s}{\sqrt{n}} = 1.9833 * \frac{10.32}{\sqrt{104}} = 2.01

The Lower Limit = 75.67 - 2.01 = 73.66

The Upper Limit = 75.67 + 2.01 = 77.68

The 95 % Confidence Interval is (73.66 , 77.68)

_______________________________________________

The mean of the data 82, 66, 91, 58, 53, 68, 72, 96, 56, 84

Average = Sum of observation / Total Obs = 726 / 10 = 72.6

The sample chosen does not seem to a good sample as the sample mean is not part of the confidence intervals.