Thread: 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.

you reject the null hypothesis and accept the alternative if........



or



Now beta=.05 when theta=10

Wait, so what are n and C? Don't you need two equations with two unknowns to find them? Where are those two equations?

FROM .....



your C is....

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?



and:



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

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