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 356 tankers is drawn. Of these ships, 246 did not have spills. Using the data, construct the 90% 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 = 356

x = 110 ( have spills each month )

Point estimate = sample proportion = = x / n = 0.309

1 - = 0.691

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

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

= 1.645 * (((0.309 * 0.691) / 356)

= 0.040

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.309 - 0.040 < p < 0.309 + 0.040

0.269 < p < 0.349

The 90% confidence interval for the population proportion of oil tankers that have spills each month is (0.269 , 0.349)