A research institute poll asked respondents if they felt vulnerable to identity

Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1002 and x=513 who said "yes." Use a 99 %99% confidence level. answer question a-d/   

a. Find the best point estimate of the population proportion p.

B. Identify the value of margin of error E. ________ (Round to four decimal places as needed)

C) Construct a confidence interval. ___ < p <. (Round to three decimal places as needed)

D) Write a statement that correctly interprets the confidence interval. Choose the correct answer bellow

a) One has 99% conficence that the interval from the lower bound to the upper boundactually does contain the true value of the population proportion.

b) 99% of sample proportions will fall between the lower bound and the upper bound.

c) there is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

d) One has 99% confidence that the sample proportion is equal to the population proportion

Explanation / Answer

a) point estimate of the population proportion p = phat = x/n = 513/1002= 0.5119

b) margin of error = E = 2.576* sqrt[(0.5119* 0.4881)/1002]

E=2.576*0.0157

E=0.0405

c) confidence interval phat + /- E

=> 0.5119-0.0405<p<0.05119+0.0405

=0.472<p<0.553

D)the answer is "A" the population proportion true value fall between 99% confidential interval

One has 99% conficence that the interval from the lower bound to the upper boundactually does contain the true value of the population proportion. So answer A is .correct.

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