Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 9 had kids. Based on this, construct a 99% confidence interval for the proportion ππ of adult residents who are parents in this county.

Give your answers as decimals, to three places.

< π <

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 9 / 100 = 0.090

1 - = 1 - 0.090 = 0.91

Z/2 = 2.576

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

= 2.576 * (((0.090 * 0.91) / 100)

Margin of error = E = 0.074

A 99% confidence interval for population proportion p is ,

- E < < + E

0.090 - 0.074 < < 0.090 + 0.074

0.016 < < 0.164