Question 1171865:
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=943 and x=579 who said "yes." Use a 99% confidence level.
a) Find the best point estimate of the population proportion p.
b)Identify the value of the margin of error E.
c) Construct the confidence interval.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (a)
The best estimate for the population proportion p is the sample proportion phat (read as "p-hat")
In this case,
phat = (number of yes responses)/(number total)
phat = x/n
phat = 579/943
phat = 0.61399787910922
phat = 0.614
Which is approximate.
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Part (b)
At 99% confidence, the z critical value is roughly z = 2.576
The margin of error is
E = z*sqrt(phat*(1-phat)/n)
E = 2.576*sqrt(0.61399787910922*(1-0.61399787910922)/943)
E = 0.040838360004
E = 0.04
This is approximate.
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Part (c)
We'll use the results of parts (a) and (b)
The lower boundary L of the confidence interval is
L = (center) - (margin of error)
L = (phat) - (E)
L = 0.61399787910922 - 0.040838360004
L = 0.57315951910522
L = 0.5732
And the upper boundary U is
L = (center) + (margin of error)
L = (phat) + (E)
L = 0.61399787910922 + 0.040838360004
L = 0.65483623911322
L = 0.6548
The 99% confidence interval in the form L < p < U is roughly 0.5732 < p < 0.6548
We can write this as (0.5732, 0.6548)
We are 99% confident that the population proportion p is between 0.5732 and 0.6548
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