Question 1005133: Suppose that a particular candidate for public office is in fact favored by 49% of all registered voters in the district. A polling organization will take a random sample of 700 voters and will use p̂, the sample proportion, to estimate p.
What is the approximate probability that p̂ will be greater than 0.5, causing the polling organization to incorrectly predict the result of the upcoming election?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that a particular candidate for public office is in fact favored by 49% of all registered voters in the district.
A polling organization will take a random sample of 700 voters and will use p̂^, the sample proportion, to estimate p.
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What is the approximate probability that p̂ will be greater than 0.5, causing the polling organization to incorrectly predict the result of the upcoming election?
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z(0.5) = (0.5-0.49)/sqrt[0.49*0.51/700] = 0.01/0.01889 = 0.5393
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P(p^>0.5) = P(z > 0.5393) = 0.2983
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Cheers,
Stan H.
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