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Math Help - sample size

  1. #1
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    sample size

    i have a formula for the sample size as
    n=A * [ ( (a+t)(1-a-t) + a(1-a) ) / t^2 ], where A, a & t are all unknown constants.
    The question is to show that n has a maximum when
    a = (1-t)/2

    I think the A can just be ignored so that I need to find the maximum of the top line and minimum of the bottom. Since the bottom is just t^2 and fixed I can't do anything with it so just need to maximise the top?
    At first I differentiated the top with respect to t and ended up with a = (1-2t)/2, although since t is constant I don't think I can do this?

    Any help would be very welcome!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: sample size

    Quote Originally Posted by bubblygirl90 View Post
    i have a formula for the sample size as
    n=A * [ ( (a+t)(1-a-t) + a(1-a) ) / t^2 ], where A, a & t are all unknown constants.
    The question is to show that n has a maximum when
    a = (1-t)/2

    I think the A can just be ignored so that I need to find the maximum of the top line and minimum of the bottom. Since the bottom is just t^2 and fixed I can't do anything with it so just need to maximise the top?
    At first I differentiated the top with respect to t and ended up with a = (1-2t)/2, although since t is constant I don't think I can do this?

    Any help would be very welcome!
    You need to differentiate the top with respect to a.
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  3. #3
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    Re: sample size

    Quote Originally Posted by alexmahone View Post
    You need to differentiate the top with respect to a.
    Ahh, so simple! Don't know why i didn't see that

    Thank you!
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