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Math Help - Statistics power function problem

  1. #1
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    Statistics power function problem

    Here's the problem, I'm stuck:

    Consider the distributions N(mu1, 400) and N(mu2, 225). Let theta = mu1-mu2 and x and y be the observed means of two independent random samples, each of size n, from these two disbtibutions. We reject H(0) : theta = 0 and accept H(a): theta >0 if and only if x-y >=C. If pi(theta) is the power function of this test, find n and C so that pi(theta=10) = 0.95 at significance level alpha = 0.05.

    Thank for anyone's help.
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  2. #2
    MHF Contributor matheagle's Avatar
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    you reject the null hypothesis and accept the alternative if........

    {X-Y-0\over\sqrt{{400\over n}+{225\over n}}}>1.645

    or

    X-Y>1.645\sqrt{{400\over n}+{225\over n}}

    Now beta=.05 when theta=10

    {X-Y-10\over\sqrt{{400\over n}+{225\over n}}}<-1.645
    Last edited by matheagle; April 12th 2010 at 05:40 PM.
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  3. #3
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    Wait, so what are n and C? Don't you need two equations with two unknowns to find them? Where are those two equations?
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  4. #4
    MHF Contributor matheagle's Avatar
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    FROM .....

    X-Y>1.645\sqrt{{400\over n}+{225\over n}}

    your C is....

    1.645\sqrt{{400\over n}+{225\over n}}
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  5. #5
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    I feel kinda dumb, but where do you get the value of n from? Do you get it by solving the following system of equations?

    <br /> <br />
{X-Y-10\over\sqrt{{400\over n}+{225\over n}}}=-1.645<br />

    and:

    <br /> <br />
X-Y=1.645\sqrt{{400\over n}+{225\over n}}<br />

    So if I subtract the first equation from the 2nd, I get: <br /> <br />
10=3.29\sqrt{{400\over n}+{225\over n}}<br />

    and n = 67.65, but since it should be a whole number, we round up to 68?
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