Question

Out of 600 people sampled, 306 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

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 306 / 600 = 0.510

1 - = 1 - 0.510 = 0.49

Z/2 = 1.96

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

= 1.96 * (((0.510 * 0.49) / 600)

Margin of error = E = 0.040

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.510 - 0.040 < p < 0.510 + 0.040

0.470 < p < 0.550

The 95% confidence interval for the population proportion p is : 0.470 , 0.550