SOLUTION: The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases. If the population proportion is p = 0.51, how large a sample is needed to red

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Question 1086392: The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases. If the population proportion is
p = 0.51,
how large a sample is needed to reduce the standard deviation of p̂ to σp hat = 0.005? (The 68−95−99.7 rule then says that about 95% of all samples will have p̂ within 0.01 of the true p. Round your answer to up to the next whole number.)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases.
If the population proportion is p = 0.51,how large a sample is needed to reduce the standard deviation of p̂ to σp hat = 0.005?
std of p-hat = s/sqrt(n)
Solve s/sqrt(n) = 0.005
sqrt(0.51*0.49/n) = 0.005
sqrt(0.51*0.49)/0.005 = sqrt (n)
0.51*0.49/0.005^2 = n
n = 9996
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(The 68−95−99.7 rule then says that about 95% of all samples will have p̂ within 0.01 of the true p. Round your answer to up to the next whole number.)
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Cheers,
Stan H.
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