Question

Out of 600 people sampled, 528 had children under the age of 18. Based on this, construct a 95% confidence interval for the true population proportion of people with children under the age of 18. Give your answers as decimals, to three places. < p

Answer 1

Solution :

Given that,

n = 600

x = 528

Point estimate = sample proportion = = x / n =528/600=0.88

1 -   = 1- 0.88 =0.12

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z 0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.88*0.12) / 600)

E = 0.026

A 95% confidence interval p is ,

- E < p < + E

0.88-0.026< p < 0.88+0.026

0.854< p < 0.906