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In: Statistics and Probability

An environmentalist wants to find out the fraction of oil tankers that have spills each month....

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.

Solutions

Expert Solution

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 )

orchestra answered 2 years ago
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