Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 201 had kids. Based on this, construct a 90% confidence interval for the proportion π of adult residents who are parents in this county. Give your answers as decimals, to three places. < π

< π <

Answer 1

Solution :

Given that,

n = 300

x = 201

Point estimate = sample proportion = = x / n = 201 / 300 = 0.670

1 - = 1 - 0.670 = 0.330

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.670 * 0.330) / 300)

= 0.045

A 90% confidence interval for population proportion p is ,

- E < < + E

0.670 - 0.045 < < 0.670 + 0.045

0.625 < < 0.715

(0.625 , 0.715)