"A single observation is taken from the Bi(2,theta) distribution. Idenitfy all eight possible tests of the hypotheses:
H0: theta = 0.5
H1: theta = 0.75
and in each case give the type 1 and 2 error probabilities. Which test is preferred?"
I am stuck on identifying the 8 tests. Is this just saying where theta could be relative to H0 and H1?
Any help most welcome, thanks.
Thanks, I am not sure if the question is not just poorly worded.
The issue I had was in listing all 8 risks; I think I am going with
H0 : theta = 0.5; H1 theta<>0.5
H0 : theta = 0.5; H1 theta>0.5
H0 : theta = 0.5; H1 theta<0.5
H0 : theta = 0.75; H1 theta<>0.75
H0 : theta = 0.75; H1 theta<0.75
H0 : theta = 0.75; H1 theta>0.75
Perhaps the last two are:
H0 : theta = 0.5; H1 theta=0.75
H0 : theta = 0.75; H1 theta=0.5
I could then work out type 1 and 2 errors based on these tests. Do you agree those are the 8 possible tests?
any comment most welcome - thanks