Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 400 adult residents sampled, 360 had kids. Based on this, construct a 95% confidence interval for the proportion, p, of adult residents who are parents in this county.

Answer 1

Solution :

Given that,

n = 400

x = 360

Point estimate = sample proportion = = x / n = 360/400=0.9

1 -   = 1-0.9 =0.1

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.9*0.1) /400 )

E = 0.029

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.9-0.029 < p < 0.9+0.029

0.871< p < 0.929