Construct a Confidence Interval- Need Help

Question

Out of 400 people sampled, 180 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to three places

I am 95% confident that the proportion of people who have kids is between ________and _________ .

Answer 1

Sample proportion (phat) = 180/400 = 0.45

z-critical value for 95% confidence interval is z-score for probability = 0.975 = 1.96

CI = phat +/- z-critical value * sqrt((phat)(1-phat)/sample size)

= 0.45 +/- 1.96 * sqrt(0.45 * 0.55/400)

= 0.45 +/- 0.049

= 0.401, 0.499