Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 150 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 = 150 / 200 = 0.750

1 - = 1 - 0.750 = 0.25

Z_{/2}
= 2.576

Margin of error = E = Z_{
/ 2} *
((
* (1 -
)) / n)

= 2.576 * (((0.750 * 0.25) / 200)

= 0.079

A 99% confidence interval for population proportion p is ,

- E < < + E

0.750 - 0.079 < < 0.750 + 0079

**0.671 <
< 0.829**

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