1. Apr 14, 2010

### bryandnk

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

and:

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

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

$$10=3.29\sqrt{{400\over n}+{225\over n}}$$

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. Apr 15, 2010

### bryandnk

no one can help?

3. Apr 16, 2010

### Hoblitz

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.