Question

Assume that a sample is used to estimate a population proportion p. Find the 99.5% confidence interval for a sample of size 274 with 184 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

99.5% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

sample proportion, = 0.6715
sample size, n = 274
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.6715 * (1 - 0.6715)/274) = 0.0284

Given CI level is 99.5%, hence α = 1 - 0.995 = 0.005
α/2 = 0.005/2 = 0.0025, Zc = Z(α/2) = 2.807

Margin of Error, ME = zc * SE
ME = 2.807 * 0.0284
ME = 0.0797

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.6715 - 2.807 * 0.0284 , 0.6715 + 2.807 * 0.0284)
CI = (0.592 , 0.751)