Question

TestScore
53
53
56
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56
58
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64
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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!

Answer 1

Answer:

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.