Confidence Intervals for a Proportion

Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 49 had kids. Based on this, construct a 99% confidence interval for the proportion  of adult residents who are parents in this county.

Give your answers as decimals, to three places.

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Answer 1

CI interval for a proportion = sample proportion (phat) +/- z-critical * sqrt(phat*(1-phat)/sample size))

Phat = 49/100 = 0.49

z-critical is z-score associated with (1 + 0.99/2) = 0.995 probability = 2.575

CI = 0.49 +/- 2.575 * sqrt(0.49*0.51/100)

= 0.49 +/- 0.129

= 0.361,0.619