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Homework Help: Please help with simple statistics problem

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data
    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.

    3. The attempt at a solution

    {X-Y-10\over\sqrt{{400\over n}+{225\over n}}}=-1.645


    [tex]C = X-Y=1.645\sqrt{{400\over n}+{225\over n}}[/tex]

    So if I subtract the first equation from the 2nd, I get:

    [tex]10=3.29\sqrt{{400\over n}+{225\over n}}[/tex]

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

    Is any of this right, or what's the correct answer?
  2. jcsd
  3. Apr 15, 2010 #2
    no one can help?
  4. Apr 16, 2010 #3
    So the first equation is from the true distribution of x - y under H(a) which is Normal(10, 625/n) due to independence.

    The second equation comes form the upper tail test of x - y, which only rejects when the test statistic is greater than (in this case) 1.645.

    Seems to me you've done this correctly; you want to round up to 68 because increasing sample size will only increase power.
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