Question 1161767: A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=985 and x=561 who said "yes." Use a 99 % confidence 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 by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the point estimate or p hat is 561/985=0.5695. That is the best estimate (the only one you have)
the 99% CI half-interval, which is E=z*sqrt(p(1-p)/n), and z=2.576
so the half-interval or margin of error E=0.0406
the CI is then 0.5695+/-0.0406
=(0.5289, 0.6101)
or to three decimal places 0.529 < p < 0.610.
What that means: the true proportion of people who feel vulnerable we do not know. But we can be highly confident, 99% confident, that the value lies between those two numbers above. It doesn't mean there is a probability, because the true value is either in or outside of the interval and we don't know which. But we are highly confident that is the interval.
If one were going to do 100 samples of the same number of people, 99 of them would contain the true value. We just wouldn't know which 99. That is where the probability fits in .
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