Question

TestScore 53 53 56 56 56 58 58 58 59 59 59 60 60 62 63...

TestScore
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

Take a random sample of 10 data values from "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!

Random Sample of size 10 taken is:

 79 74 72 68 80 90 96 83 81 64

Sample mean using excel function AVERAGE(), x̅ = 78.7

Sample standard deviation using excel function STDEV.S(), s = 9.7188

Sample size, n = 10

95% Confidence interval :

At α = 0.05 and df = n-1 = 9, two tailed critical value, t-crit = T.INV.2T(0.05, 9) = 2.262

Lower Bound = x̅ - t-crit*s/√n = 78.7 - 2.262 * 9.7188/√10 = 71.75

Upper Bound = x̅ + t-crit*s/√n = 78.7 + 2.262 * 9.7188/√10 = 85.65

71.75 < µ < 85.65

The confidence interval of sample is wider than the population.