Question

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.

Suppose a sample of 779 tankers is drawn. Of these ships, 233 had spills. Using the data, construct the 95% 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 = 779

x = 233

Point estimate = sample proportion = = x / n = 233/779=0.299

1 - = 1-0.299=0.701

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

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

= 1.96 (((0.299*0.701) / 779)

E = 0.032

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.299-0.032 < p <  0.299+0.032

0.267< p < 0.331

The 95% confidence interval for the population proportion p is : 0.267,0.331