Question

Out of 500 people sampled, 195 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to four places

answer ____ < p < answer _____

Answer 1

Solution :

Given that,

n = 500

x = 195

Point estimate = sample proportion = = x / n = 195/500=0.39

1 - = 1-0.39=0.61

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =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 (((0.39*0.61) / 500)

E = 0.0428

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.39-0.0428< p < 0.39+0.0428

0.3472< p < 0.4328

The 95% confidence interval for the population proportion p is : 0.3472< p < 0.4328