Question

an environmentalist wants to find out the fraction 438 tankers step

An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 2 of 2: Suppose a sample of 438 tankers is drawn. Of these ships, 311 did not have 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. Tables Keypa Answer How to enter your answer Previous step ans Lower endpoint Upper endpoint

Answer 1

We know that population proportion confidence interval is given by:

p = Za/ 23 p(1-P) n

where based on the sample

$\hat{p} = \frac{x}{n}$

where x is the no of success

and

n is the number of total observations.

x = 438 - 311 = 127 (Since we need to find the CI for oil tankers that have spills)

n = 438

So based on the sample of ghost CI is given by:

127 P= = 0.2922374

= 0,05

and

$Z_{\alpha/2}$ is the critical value at $\alpha$ level of significance.

Which we have calculated in R

> qnorm(0.975) [1] 1.959964

So 95% Confidence interval is given by:

$0.2922374 \pm 1.96 \sqrt{\frac{0.2922374(1-0.2922374)}{438}}$

(0.25,  0.335)

So 95% CI is (0.25,  0.335)

lower endpoint = 0.25

upper endpoint = 0.335

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