Question

In a survey of 1000 US adults, twenty percent say they never exercise. Find a 99% confidence interval for the proportion of US adults who say they never exercise. Does the scenario represent a confidence interval or a hypothesis test?

Answer 1

This is confidence interval scenario

sample proportion, = 0.2
sample size, n = 1000
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.2 * (1 - 0.2)/1000) = 0.0126

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

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.2 - 2.58 * 0.0126 , 0.2 + 2.58 * 0.0126)
CI = (0.1675 , 0.2325)