SOLUTION: The Academy of Orthopedic surgeons states that 90% of U.S women wear shoes that are too small for their feet. A researcher wants to be 95% confident that this proportion is within

Question 189512: The Academy of Orthopedic surgeons states that 90% of U.S women wear shoes that are too small for their feet. A researcher wants to be 95% confident that this proportion is within 2% of the true proportion. How large a sample is necessary?
Can you please show me how you get the answer? Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Academy of Orthopedic surgeons states that 90% of U.S women wear shoes that are too small for their feet. A researcher wants to be 95% confident that this proportion is within 2% of the true proportion. How large a sample is necessary?
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Since E = z*sqrt(pq/n)
sqrt(n) = [z*sqrt(pq)]/E
And n = [z/E]^2*pq
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Your problem:
n = [1.96/0.02]^2*(0.9*0.1) = 864.36
Rounding up n = 865
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Cheers,
Stan H.
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