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 292 tankers is drawn. Of these ships, 234 did not have spills. Using the data, construct the 80% confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places. Lower endpoint:__________ Upper endpoint:__________

Answer 1

Solution:

Given:

Sample Size = n = 292

Number of ships did not have spills = 234

Then

x = Number of oil tankers that had spills = 292 - 234 = 58

We have to find  the proportion of oil tankers that had spills.

Thus sample proportion is given by:

We have to  construct the 80% confidence interval for the population proportion of oil tankers that have spills each month.

Formula:

where

For 80% confidence interval

For c = 80% , find area = ( 1 + c) / 2 = ( 1+0.80) / 2 = 1.80 /2 = 0.90

Look in z table for area = 0.9000 or its closest area and find z value:

Area 0.8997 is closest to 0.9000 and it corresponds to 1.2 and 0.08

thus z = 1.28

Thus

Thus

Lower endpoint =  

Lower endpoint = 0.169

and

Upper endpoint =

Upper endpoint = 0.229