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Math Help - [SOLVED] How to find the sample size?

  1. #1
    Lok
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    [SOLVED] How to find the sample size?

    Hello, this question seems rather simple but for some reason I can't see what to use to solve it.

    Question : We want to do a study to determine the proportion of urban owners that have more than 1 computer.
    I need to find the sample size to be certain at 99% that the estimation will be at most 3% of the real proportion.

    A friend of mine suggested to use
    n = \frac{Z_{\alpha/2} * p * (1-p)}{c^{2}}

    where n is the sample size, Z_{\alpha/2} the value of Z, p the proportion and c the margin error.

    So for my problem:
    n = \frac{2.58^2*p*(1-p)}{c^{2}} = \frac{2.58^2*0.5^2}{c^2} = 1849

    My 3 questions:
    a) Is it the right formula? if so where does it come from?
    b) Why do we use p=0.5 when we have no clue what the proportion is going to be?
    c) Why do we take the value of Z as a bilateral test (hence the Z_{\alpha/2} instead of Z_{\alpha})?

    Thanks (:
    Last edited by Lok; April 13th 2009 at 10:13 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    use p=.5 when you have no idea of the range of p
    you're getting the max of p(1-p) which you can prove via calculus 1
    z=2.576 (via the t-table, or use the online stat calculators)
    and you want a two sided CI since you want the sample and true proportion to be within .03 of each other.
    Last edited by matheagle; April 13th 2009 at 10:49 PM.
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