Out of 240 people sampled, 60 had kids. Based on this, construct a 95% confidence

Question

Out of 240 people sampled, 60 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Answer 1

CI = sample proportion +/- z-critical value * standard error

sample proportion (phat) = 60/240 = 0.25

standard error = sqrt(phat*(1-phat)/sample size) = sqrt(0.25*0.75/240) = 0.028

z-critical value (alpha/2 = 0.025, find z-score for probability 0.975) = 1.96

CI = 0.25 +/- 1.96 * 0.028 = 0.195, 0.305