Question

Out of 300 people sampled, 270 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 three places.

___________ < p < _______________

Answer 1

Solution :

Given that,

n = 300

x = 270

Point estimate = sample proportion = = x / n = 270/300=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) /300 )

= 0.0339

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.9- 0.0339< p <0.9+ 0.0339

0.8661< p < 0.9339

0.866< p < 0.934