The 1996 gss 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 720 respondents, 578 said yes. (a) find a 95% confidence interval for the population proportion who would say yes. round to two decimal places.

The confidence interval would be
.

We use the formula
, where

, with p being the sample proportion and N being the sample size.

First we find the z-score associated with this level of confidence:
Convert 95% to a decimal:  95/100 = 0.95
Subtract from 1:  1-0.95 = 0.05
Divide by 2:  0.05/2 = 0.025
Subtract from 1:  1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.

Since 578/720 said yes, this gives us p=0.80:


This gives us