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=1040 and x=544 who said yes.

Use a 95% confidecne level.

A. find the best point of estimate of the population of portion p. B. Identify the value of the margin of error E. E= round to four decimal places as needed. C. Construct the confidence interval. _ < p <_ round to three decimal places. D. Write a statement that correctly interprets the confidence interval.

Answer 1

Given : n=1040 , X=544

a) The point estimate is ,

Point estimate=

х 544 p= 0.5231 n 1040

b) Now , the critical value is ,

; From Z-table

Za a/2 20.05/2 1.96

The margin of error is ,

$E=Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=1.96*\sqrt{\frac{0.5231(1-0.5231)}{1040}}=0.0304$

c) The 95% confidence interval is ,

$\hat{p}\pm E$

0.5231 +0.0304