Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 80 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 80 / 500 = 0.16

Z_/2 = 1.645

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

= 1.645 * (((0.16 * 0.84) / 500)

= 0.027

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.16 - 0.027 < p < 0.16 + 0.027

0.133 < p < 0.187

(0.133 , 0.187)