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=1016 and x=577 who said​ "yes." Use a 99% 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.   E= ​(Round to three decimal places as​ needed.)   ​c) Construct the confidence interval.   __

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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=1016
and
x=577
who said​ "yes." Use a
99%
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.
 
E=
​(Round to three decimal places as​ needed.)
 
​c) Construct the confidence interval.
 
__<p<__
​(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.
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.
 
C.
99​%
of sample proportions will fall between the lower bound and the upper bound.
 
D.
There is a
99​%
chance that the true value of the population proportion will fall between the lower bound and the upper bound.
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