Question

An environmentalist wants to find out the fraction of oil tankers that have spills each month. Suppose a sample of 836 tankers is drawn. Of these ships, 577 did not have spills. Using the data, construct the 99% confidence interval for the population proportion of oil tankers that have spills each month.

Answer 1

Answer:

The 99% confidence interval for the population proportion of oil tankers that have spills each month.

(0.6489 , 0.7311)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 836

Suppose a sample of 836 tankers is drawn. Of these ships, 577 did not have spills.

sample proportion

                    $p^{-} = \frac{x}{n} = \frac{577}{836} = 0.690$

The 99% confidence interval for the population proportion is determined by

$(p^{-} - Z_{0.01} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.01} \sqrt{\frac{p(1-p)}{n} })$

Step(ii):-

The Z- value = 2.576

$(0.690 - 2.576 \sqrt{\frac{0.690(1-0.690)}{836} } , 0.690 + 2.576 \sqrt{\frac{0.690(1-0.690)}{836} })$

On calculation , we get

(0.690 -  0.0411 , 0.690 + 0.0411)

(0.6489 , 0.7311)

Final answer:-

The 99% confidence interval for the population proportion of oil tankers that have spills each month.

(0.6489 , 0.7311)