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 1344 tankers is drawn. Of these ships, 255 had 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,

n = 1344

x = 255

= x / n =255 /1344 = 0.190

1 - = 1 - 0.190 = 0.810

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.190 * 0.810) / 1344) = 0.028

A 99% confidence interval for population proportion p is ,

- E < P < + E

0.190 - 0.028 < p < 0.190 + 0.028

0.162 < p < 0.218

The 99% confidence interval for the population proportion p is : ( 0.162 , 0.218)