Statstics problem

Question

Out of 200 people sampled, 92 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Answer 1

The sample proportion p_hat = 92 / 200 = 0.46

Our confidence interval is

p_hat ± z* x S.E.

where z* is our z-score based on the confidence level. For 95%, our z* = 1.96

S.E. is the standard error, and is calculated as √ [p_hat x (1 - p_hat) / n]

S.E. = √ [0.46 x (0.54) / 200 = 0.0352

so our 95% CI is

0.46 ± 1.96 x 0.0352 = 0.46 ± 0.0691 = (0.391, 0.529)