Question

Problem 3

In May of 1984, 834 Americans were asked in a poll whether they thought the Olympics reduced international tension, increased international tension, or neither; 425 of them said they thought the Olympics reduced international tension.3 Calculate a 97.5% confidence interval for the proportion of Americans who believed this.

1I’m learning Welsh.

2Yes, there were 50 states at the time, but the majority of the electoral votes in both Alabama and Mississippi went to third-party candidates.

3The proportion is correct; the numbers themselves are realistic but fictitious.

Answer 1

sample proportion, = 0.5096
sample size, n = 834
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.5096 * (1 - 0.5096)/834) = 0.0173

Given CI level is 97.5%, hence α = 1 - 0.975 = 0.025
α/2 = 0.025/2 = 0.0125, Zc = Z(α/2) = 2.24

Margin of Error, ME = zc * SE
ME = 2.24 * 0.0173
ME = 0.0388

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.5096 - 2.24 * 0.0173 , 0.5096 + 2.24 * 0.0173)
CI = (0.4708 , 0.5484)