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=1096 and x=542 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

Explanation:

Given that a research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1096 and x=542 who said yes.

i.e. sample size =
`n=1096\\`

who said yes =
`x=542\\`

Sample proportion =
`p=(542)/(1096) =0.4945`

Std error of proportion =
`\sqrt{(p(1-p))/(n) } \\=\sqrt{(0.4945(1-0.4945))/(1096) } \\=0.0151`

Margin of error 95%
`= 1.96 (se)\\=0.0296`

Hence confidence interval for proportions

=
`(0.4945-0.0296, 0.4945+0.0296)\\= (0.4649,0.5241)`

a) Point estimate
`=0.4945`

B) Margin of error =
`0.0296`

C) Conf interval =
`(0.4649,0.5241`

D) We are 95% confident that for large random samples representing the population, the proportion of yes will lie between these two values.