Out of 300 people sampled, 264 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.

Question

Out of 300 people sampled, 264 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

To construct a 95% confidence interval for the true population proportion of people with kids, we can use the following formula:

p̂ ± z*(√p̂(1-p̂)/n)

where p̂ is the sample proportion (264/300 = 0.880), z is the z-score for a 95% confidence level (1.96), and n is the sample size (300).

Plugging in the values, we get:

0.880 ± 1.96 * (√0.880(1-0.880)/300)

= 0.880 ± 0.038

Therefore, the 95% confidence interval for the true population proportion of people with kids is:

0.880 ± 0.038 = (0.842, 0.918)

Rounded to three decimal places, the 95% confidence interval is (0.842, 0.918).