Question

Out of 600 people sampled, 570 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Enter your answer as ˆ p ± m p ^ ± m Give your answers as decimals, to three places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 570 / 600 = 0.95

1 - = 1 - 0.95 = 0.05

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.95 * 0.05) / 600 )

= 0.017

A 95% confidence interval for population proportion p is ,

± m

= 0.95 ± 0.017

= 0.933, 0.967 )