Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 20 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county.

Give your answers as decimals, to three places.

<p <<p <

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 20 / 200 = 0.100

1 - = 1 - 0.100 = 0.9

Z/2 = 1.645

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

= 1.645 * (((0.100 * 0.9) / 200)

Margin of error = E = 0.035

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.100 - 0.035 < p < 0.100 + 0.035

0.065 < p < 0.135