Question 530182: 2. Which would be hardest for you to give up: Your computer or your television? In a recent survey of 1677 U.S. Internet users, 74% of the young tech elite (average age of 22) say their computer would be very hard to give up (PC Magazine, February 3, 2004). Only 48% say their television would be very hard to give up.
a.Develop a 95% confidence interval for the proportion of the young tech elite that would find it very hard to give up their computer.
b.Develop a 99% confidence interval for the proportion of the young tech elite that would find it very hard to give up their television.
c.In which case, part (a) or part (b), is the margin of error larger? Explain why.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Which would be hardest for you to give up: Your computer or your television?
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In a recent survey of 1677 U.S. Internet users, 74% of the young tech elite (average age of 22) say their computer would be very hard to give up.
a.Develop a 95% confidence interval for the proportion of the young tech elite that would find it very hard to give up their computer.
The sample proportion = 0.74
Margin of Error = 1.96*sqrt{0.74*0.26/1677] = 0.02
95% CI: 0.74-0.-02 < p < 0.74+0.02
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Only 48% say their television would be very hard to give up.
b.Develop a 99% confidence interval for the proportion of the young tech elite that would find it very hard to give up their television.
The sample proportion = 0.48
99% Margin of Error = 2.5758*sqrt[0.48*0.52/1677] = 0.03
99%CI: 0.48-0.03 < p < 0.48+0.03
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c.In which case, part (a) or part (b), is the margin of
error larger? Explain why.
Ans: b, because the Margin of error is larger.
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Cheers,
Stan H.
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