Question

use the sample data and confidence level given below to complete parts (a) through (d).
a research institute poll asked respondents if they felt vulnerable to identity theft. in the poll, ( n = 904 ) and ( x = 576 ) who said \yes.\ use a 90% confidence level.
click the icon to view a table of z scores.
a) find the best point estimate of the population proportion ( p ).
0.637
(round to three decimal places as needed.)
b) identify the value of the margin of error ( e ).
( e=square )
(round to three decimal places as needed.)

Explanation:

Step1: Calculate $\hat{q}$

The formula for $\hat{q}$ is $\hat{q}=1 - \hat{p}$. Given $\hat{p}=\frac{x}{n}=\frac{576}{904}\approx0.637$, then $\hat{q}=1 - 0.637 = 0.363$.

Step2: Find $z_{\alpha/2}$

For a 90% confidence level, $\alpha=1 - 0.90=0.10$, and $\alpha/2 = 0.05$. From the z - score table, $z_{\alpha/2}=z_{0.05}=1.645$.

Step3: Calculate the margin of error $E$

The formula for the margin of error $E$ for a proportion is $E = z_{\alpha/2}\sqrt{\frac{\hat{p}\hat{q}}{n}}$.
Substitute $\hat{p}=0.637$, $\hat{q}=0.363$, $n = 904$, and $z_{\alpha/2}=1.645$ into the formula:

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Answer:

$E = 0.026$