Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 400 adult residents sampled, 128 had kids. Based on this, construct a 99% confidence interval for the proportion p of adult residents who are parents in this county.

Express your answer in tri-inequality form. Give your answers as decimals, to three places.

____ < p < ____ Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.

p = ____ ± ____

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 128 / 400 = 0.320

Z_/2 = 2.576

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

= 2.576 * (((0.320 * 0.680) / 400)

= 0.060

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.320 - 0.060 < p < 0.320 + 0.060

0.260 < p < 0.380

p = 0.320 0.060