1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook