I did this problem and I got the sample size to equal 351.31,but the answer prov

Question

I did this problem and I got the sample size to equal 351.31,but the answer provided to me was .666. I cannot see where thisanswer comes from.

A specialist in industrial medicine wants to determine whatproportion of all shoe factories require an employee to provide adoctor’s certificate for 3 or more days’ absence forillness. What size sample should the researcher take in order to bewithin 5% of the true population proportion with 99% confidence?The researcher feels that the true proportion can not be more than3%. I did this problem and I got the sample size to equal 351.31,but the answer provided to me was .666. I cannot see where thisanswer comes from.

A specialist in industrial medicine wants to determine whatproportion of all shoe factories require an employee to provide adoctor’s certificate for 3 or more days’ absence forillness. What size sample should the researcher take in order to bewithin 5% of the true population proportion with 99% confidence?The researcher feels that the true proportion can not be more than3%.

Explanation / Answer

=.01 /2=.005 Z.005=2.576 e=.05 phat=.03 qhat=.77 n=(2.576)2(.03)(.97)/.052=77.24 So choose n=78

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