Question

1: In a randomly selected sample of 500 registered voters in a community, 340 individuals say that they plan to vote for Candidate Y in the upcoming election. Find a 95% confidence interval for the proportion of the registered voter population who plan to vote for Candidate Y. (Round your answers to three decimal places.)

2: Math 153 Statistical reasoning

Answer 1

sample proportion, pcap = 340/500 = 0.68
sample size, n = 500
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.68 * (1 - 0.68)/500) = 0.0209

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.68 - 1.96 * 0.0209 , 0.68 + 1.96 * 0.0209)
CI = (0.639 , 0.721)