document.write( "Question 1086392: The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases. If the population proportion is
\n" ); document.write( "p = 0.51,
\n" ); document.write( " 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.) \n" ); document.write( "

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The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases.
\n" ); document.write( "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?
\n" ); document.write( "std of p-hat = s/sqrt(n)
\n" ); document.write( "Solve s/sqrt(n) = 0.005
\n" ); document.write( "sqrt(0.51*0.49/n) = 0.005
\n" ); document.write( "sqrt(0.51*0.49)/0.005 = sqrt (n)
\n" ); document.write( "0.51*0.49/0.005^2 = n
\n" ); document.write( "n = 9996
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\n" ); document.write( "(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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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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