(HW 8 Q2) Use the sample data and confidence level given below to complete parts

Question

(HW 8 Q2) 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= 978 and x= 569 who said "yes". Use a 95% confidence level.
a) find the best point estimate of the population p (Round to three decimal places as needed) b)Identify the value of the margin of error E (Round to fourdecimal places as needed) C) Construct the the confidence inerval   (Round to three decimal places as needed d) write the statement that correctly interprets the confidence interval .
(HW 8 Q2) 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= 978 and x= 569 who said "yes". Use a 95% confidence level.
a) find the best point estimate of the population p (Round to three decimal places as needed) b)Identify the value of the margin of error E (Round to fourdecimal places as needed) C) Construct the the confidence inerval   (Round to three decimal places as needed d) write the statement that correctly interprets the confidence interval .
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= 978 and x= 569 who said "yes". Use a 95% confidence level.
a) find the best point estimate of the population p (Round to three decimal places as needed) b)Identify the value of the margin of error E (Round to fourdecimal places as needed) C) Construct the the confidence inerval   (Round to three decimal places as needed d) write the statement that correctly interprets the confidence interval .

Explanation / Answer

a) mean ,x=569

sample size,n = 978

sample proportion = x/n = 569/978 = 0.5817

b) Margin of Error = Z a/2 Sqrt(p*(1-p)/n))x

Margin of Error = 1.96 * ( Sqrt ( (0.5817*0.4183) /978) )

=0.0309

c) Confidence Interval For ProportionCI = p ± Z a/2 Sqrt(p*(1-p)/n)))

Confidence Interval = [ 0.5817 ±Z a/2 ( Sqrt ( 0.5817*0.4183) /978)]

                                = [0.5507, 0.6126 ]

d) It lies b/w 55% to 61%

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