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 = 1033 ) and ( x = 593 ) who said \yes.\ use a ( 95% ) confidence level. a) find the best point estimate of the population proportion ( p ). (round to three decimal places as needed.) b) identify the value of the margin of error ( e ). ( e = 0.030 ) (round to three decimal places as needed.) c) construct the confidence interval. ( square < p < square ) (round to three decimal places as needed.)

Explanation:

Step1: Find the best - point estimate of the population proportion \(p\)

The best - point estimate of the population proportion \(p\) is the sample proportion \(\hat{p}\). The formula for \(\hat{p}\) is \(\hat{p}=\frac{x}{n}\), where \(x = 593\) and \(n=1033\).
\(\hat{p}=\frac{593}{1033}\approx0.574\)

Step2: Identify the value of the margin of error \(E\)

The margin of error \(E = 0.030\) (given)

Step3: Construct the confidence interval

The formula for the confidence interval for a proportion is \(\hat{p}-ESubstitute \(\hat{p}=0.574\) and \(E = 0.030\) into the formula:
\(0.574-0.030\(0.544

Answer:

a) \(0.574\)
b) \(E = 0.030\)
c) \(0.544