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 = 0.026 )
(round to three decimal places as needed.)
c) construct the confidence interval.
( square < p < square )
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for confidence interval

The formula for a confidence interval for a population proportion is $\hat{p}-E < p <\hat{p}+E$, where $\hat{p}$ is the point - estimate and $E$ is the margin of error.

Step2: Substitute the given values

We are given that $\hat{p}=0.637$ and $E = 0.026$.

Substitute these values into the formula:
For the lower bound: $0.637-0.026$
For the upper bound: $0.637 + 0.026$

Step3: Calculate the bounds

Lower bound: $0.637-0.026=0.611$
Upper bound: $0.637+0.026=0.663$

Answer:

$0.611 < p < 0.663$