Question

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

Step 1 of 2:

Suppose a sample of 292 tankers is drawn. Of these ships, 58 had spills. Using the data, estimate the proportion of oil tankers that had spills. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2:

Suppose a sample of 292 tankers is drawn. Of these ships, 58 had 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.

Answer 1

Solution :

Given that,

n = 292

x = 58

= x / n =58 /292 = 0.199

1 - = 1 - 0.199= 0.801

proportion   = 0.199

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z_/2 = Z_0.10 = 1.282

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

= 1.282 * (((0.199 * 0.801) / 292) = 0.030

A 80 % confidence interval for population proportion p is ,

- E < P < + E

0.199 - 0.030< p < 0.199 + 0.030

0.169 < p < 0.229

The 80% confidence interval for the population proportion p is : ( 0.169 , 0.229)