Question

If, based on a sample size of 200, a political candidate found that 125 people would vote for her in a two-person race, what is the 99% confidence interval for her expected proportion of the vote? Would she be confident of winning based on this poll? Use the appropriate formula and verify your result using the confidence intervals workbook.

Answer 1

sample proportion, = 0.625
sample size, n = 200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.625 * (1 - 0.625)/200) = 0.0342

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0342
ME = 0.0882

CI = (0.625 - 2.58 * 0.0342 , 0.625 + 2.58 * 0.0342)
CI = (0.5368 , 0.7132)