Question 1133949: 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 equals 1011 and x equals 582 who said "yes." Use a 90 % confidence level.
a) Find the best point estimate of the population proportion p.
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E =
(Round to three decimal places as needed.)
c) Construct the confidence interval.
(Round to three decimal places as needed.)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
A.
One has 99% confidence that the sample proportion is equal to the population proportion.
B.
There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
C.
One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
99% of sample proportions will fall between the lower bound and the upper bound.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x bar is 582/1011=0.576 point estimate
error is z(0.95)*sqrt(p*(1-p)/n)=1.645*sqrt(0.000242)=0.026
the 90%CI is (0.550, 0.602)
One has 99% confidence that the true value of the population mean falls in this interval. A is wrong because it has to do with the parameter, not the statistic. B uses "chance," not confidence, and is wrong.
C is correct.
D, if that is truly D, is not correct. 99% of the confidence intervals constructed will contain the true population interval, but one doesn't know which 99.
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