Question

An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 2 of 2 : Suppose a sample of 712 tankers is drawn. Of these ships, 570 did not have spills. Using the data, construct the 99% confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places.

Answer #1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 142 / 712 = 0.199

Z_{/2}
= 2.576

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

= 2.576 * (((0.199 * 0.801) / 712)

= 0.038

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.199 - 0.038 < p < 0.199 + 0.038

0.161 < p < 0.237

(0.161 , 0.237)

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