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

Answer:

Step-by-step 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 = $p=\frac{542}{1096} =0.4945$

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

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.