Question

A survey of a random sample of 1,500 young Americans found that 87% had earned their high school diploma. Based on these results, the 95% confidence interval for the proportion of young Americans who have earned their high school diploma is (0.853,0.887) What is the margin of error for this confidence interval?

Answer 1

Answer: 0.017

Step-by-step explanation:

The confidence interval for population proportion p is given by :-

$\hat{p}-E<p<\hat{p}+E$, where E is the margin of error.

Given : The proportion of the sample of young Americans earned their high school diploma : $\hat{p}=0.87$

The 95% confidence interval for the proportion of young Americans who have earned their high school diploma is (0.853,0.887) .

i.e.

$\hat{p}-E=0.853\ ----------(1)\\\\ \hat{p}+E=0.887----------(2)$

Subtract equation (1) from (2) , we get

$2E=0.034\\\\\Rightarrow\ E=0.017$

Hence, the margin of error for this confidence interval =0.017