Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 215 had kids. Based on this, construct a 95% confidence interval for the proportion p of adult residents who are parents in this county. Give your answers as decimals, to three places.

< p

Answer 1

Solution :

Given that,

n = 500

x = 215

Point estimate = sample proportion = = x / n = 215/500=0.43

1 - = 1-0.43=0.57

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

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

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

= 1.96 (((0.43*0.57) / 500)

E = 0.043

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.43-0.043 < p <0.43+ 0.043

0.387< p < 0.473

The 95% confidence interval for the population proportion p is : 0.387, 0.473