In: Statistics and Probability
An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 2 of 2 : Suppose a sample of 669 tankers is drawn. Of these ships, 529 did not have spills. Using the data, construct the 98% confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places. previous answer is .209.
Solution :
Given that,
n = 669
x = 669 - 529 = 140
Point estimate = sample proportion = = x / n = 140 / 669 = 0.209
1 - = 1 - 0.209 = 0.791
At 98% confidence level
= 1 - 98%
=1 - 0.98 =0.02
/2
= 0.01
Z/2
= Z0.01 = 2.326
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.326 (((0.209 * 0.791) / 669)
= 0.037
A 98% confidence interval for population proportion p is ,
± E
= 0.209 ± 0.037
= ( 0.172, 0.246 )