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: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 = [tex]n=1096\\[/tex]who said yes =[tex]x=542\\[/tex]Sample proportion = [tex]p=\frac{542}{1096} =0.4945[/tex]Std error of proportion = [tex]\sqrt{\frac{p(1-p)}{n} } \\=\sqrt{\frac{0.4945(1-0.4945)}{1096} } \\=0.0151[/tex]Margin of error 95% [tex]= 1.96 (se)\\=0.0296[/tex]Hence confidence interval for proportions=[tex](0.4945-0.0296, 0.4945+0.0296)\\= (0.4649,0.5241)[/tex]a) Point estimate [tex]=0.4945[/tex]B) Margin of error = [tex]0.0296[/tex]C) Conf interval = [tex](0.4649,0.5241[/tex]D) We are 95% confident that for large random samples representing the population, the proportion of yes will lie between these two values.