Question

In a poll of 1000 American adults conducted on August 5-9, 2010, 44% (p¯=0.44) of respondents approve the job that President Barack Obama was doing handling the economy. The goal is to construct a 90% confidence interval for the percentage (p) of American adults who approved of Barack Obama's handling of the economy around the period the poll was conducted. The standard error (SE) of p¯p¯ is

(A) 0.016
(B) 0.44
(C) 0.0002
(D) 0.0004

Answer 1

Answer: A) 0.016

Step-by-step explanation:

The standard error is also known as the standard deviation of sampling distribution.

Formula : $S.E.=\sqrt{\dfrac{\overline{p}(1-\overline{p})}{n}}$

Given : The proportion of respondents approve the job that President Barack Obama was doing handling the economy : $\overline{p}=0.44$

Sample size : n= 1000

Then, the standard error (SE) of $\overline{p}$ is

$S.E.=\sqrt{\dfrac{0.44(1-0.44)}{1000}}\\\\=\sqrt{0.0002464}\\\\=0.0156971\approx0.016$

Hence, the standard error (SE) of $\overline{p}$ is 0.016 .