The 1996 General Social Survey asked If the husband in a fam

The 1996 General Social Survey asked, \"If the husband in a family wants children, but the wife decides that she does not want any children, is it all right for the wife to refuse to have children?\" Of the sample of subjects asked this question, 82.7% said yes.

(a) If the standard error is 0.014, find a 97 % confidence interval for the population proportion who would say yes.

Solution

Given a=1-0.97= 0.03, Z(0.03/2)=2.17 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.827 - 2.17*0.014 = 0.797

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.827 + 2.17*0.014=0.857