you reject the null hypothesis and accept the alternative if........
or
Now beta=.05 when theta=10
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.
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?