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The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small...

The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 95% confident that this proportion is within 3% of the true proportion. How large a sample is necessary?

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The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 95% confident that this proportion is within 3% of the true proportion. How large a sample is necessary?

Given,

p = 0.8

z for 95% confidence interval = = 1.96

Margin of error =

or

0.03 =

0.03 =

n = 682.933689

n = 683

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