Question

In a survey of 1066 adults, a poll​ asked, "Are you worried or not worried about having enough money for​ retirement?" Of the 1066 surveyed, 630 stated that they were worried about having enough money for retirement. Construct a 95​%confidence interval for the proportion of adults who are worried about having enough money for retirement.

A 95​% confidence interval for the proportion of adults who are worried about having enough money for retirement is? (? ​,?​).

Answer 1

sample proportion, = 0.591
sample size, n = 1066
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.591 * (1 - 0.591)/1066) = 0.0151

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

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0151
ME = 0.03

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.591 - 1.96 * 0.0151 , 0.591 + 1.96 * 0.0151)
CI = (0.5614 , 0.6206)