Question

Small Sample Mean Problem. Each year the Heritage Foundation creates an Index of Economic Freedom for countries around the word based on assessments of freedom on property rights, corruption, business freedom, and labor freedom, among many others. We have a sample of 31 countries taken from the 2016 data. The following is a summary of this sample. Economic Freedom Leaf STEM 61.174 Мean 4 4* 64 5 09 18 22 24 32 42 Median 60.000 Min 46.400 5* 60 65 74 75 76 77 91 93 6 00 02 12 19 22 30 31 6 59 66 75 87 Маx 77.700 63.004 Variance Std Deviaton 7.938 7 26 39 43 7* 54 77 CV 12.975 Count 31 8 A value of 4 |64 is an index of 46 .4 If we constructed a 99% Confidence around this sample estimate of Economic Freedom, what would be the Bound of Error? 57.253 to 65.095 2.912 2.750 3.921

Answer 1

sample mean, xbar = 61.174
sample standard deviation, s = 7.938
sample size, n = 31
degrees of freedom, df = n - 1 = 30

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.75

ME = tc * s/sqrt(n)
ME = 2.75 * 7.938/sqrt(31)
ME = 3.921