Question

Many celebrities and public figures have Twitter accounts with large numbers of followers. However, some of these followers are fake, resulting from accounts generated by spamming computers. In a sample of 53 twitter audits, the mean percentage of fake followers was 13.3 with a standard deviation of 9.8

a) Construct a 99.8% interval for the mean percentage of fake Twitter followers. Round the answers to one decimal place.

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Answer 1

sample mean, xbar = 13.3
sample standard deviation, s = 9.8
sample size, n = 53
degrees of freedom, df = n - 1 = 52

Given CI level is 99.8%, hence α = 1 - 0.998 = 0.002
α/2 = 0.002/2 = 0.001, tc = t(α/2, df) = 3.255

ME = tc * s/sqrt(n)
ME = 3.255 * 9.8/sqrt(53)
ME = 4.382

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (13.3 - 3.255 * 9.8/sqrt(53) , 13.3 + 3.255 * 9.8/sqrt(53))
CI = (8.9 , 17.7)