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 equals 944 and x equals 575 who said​ "yes." Use a 99 % confidence level. LOADING... Click the icon to view a table of z scores. ​a) Find the best point estimate of the population proportion p. . 609 ​(Round to three decimal places as​ needed.) ​b) Identify the value of the margin of error E. E equals = nothing ​(Round to three decimal places as​ needed.) c) construct the confidence interval

Answer 1

Solution :

Given that,

n = 944

x = 575

Point estimate = sample proportion = = x / n = 575 / 944 = 0. 609

1 - = 1 - 0.609 = 0.391

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z _0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.609 * 0.391 ) / 944 )

= 0.04

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.609 - 0.04 < p < 0.609 + 0.04

0.569  < p < 0.649  

The 99% confidence interval for the population proportion p is : 0.569 , 0.649