Question

use the sample data and confidence level given below to complete parts (a) through (c). a research institute poll asked respondents if they felt vulnerable to identity theft. in the poll, n = 978 and x = 525 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. 0.537 (round to three decimal places as needed.) b) identify the value of the margin of error e. e = 0.041 (round to three decimal places as needed.) c) construct the confidence interval. < p < (round to three decimal places as needed.)

Explanation:

Step1: Recall confidence - interval formula

The confidence - interval for a population proportion $p$ is given by $\hat{p}-E

Step2: Identify given values

We are given that $\hat{p}=0.537$ and $E = 0.041$.

Step3: Calculate the lower and upper bounds

The lower bound is $\hat{p}-E=0.537 - 0.041=0.496$.
The upper bound is $\hat{p}+E=0.537+ 0.041=0.578$.

Answer:

$0.496 < p < 0.578$