Question

use the sample data and confidence level given below to complete parts (a) through (d).
in a study of cell phone use and brain hemispheric dominance, an internet survey was e - mailed to 2595 subjects randomly selected from an online group involved with ears. 931 surveys were returned. construct a 90% confidence interval for the proportion of returned surveys.
click the icon to view a table of z scores.
b) identify the value of the margin of error e.
e = 0.015
(round to three decimal places as needed.)
c) construct the confidence interval.
<p<
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion $\hat{p}$

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 931$ (number of returned surveys) and $n=2595$ (total number of surveys sent). So, $\hat{p}=\frac{931}{2595}\approx0.359$.

Step2: Construct the confidence interval

The formula for a confidence interval for a proportion is $\hat{p}-E < p<\hat{p} + E$. We know that $\hat{p}\approx0.359$ and $E = 0.015$ (from part b).
Substitute the values: $(0.359 - 0.015)

Answer:

$0.344 < p<0.374$