Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 400 adult residents sampled, 156 had kids. Based on this, construct a 95% confidence interval for the proportion ππ of adult residents who are parents in this county.

Give your answers as decimals, to three places

Answer 1

Solution :

Point estimate () = x / n = 156 / 400 = 0.39

1 - = 0.61

Z/2 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * ((0.39 * 0.61) / 400)

= 0.048

A 95% confidence interval for population proportion is ,

- E < < + E

0.39 - 0.048 < < 0.39 + 0.048

0.342 < < 0.438