# Hypothesis tests

• Aug 9th 2010, 12:05 PM
sharpe
Hypothesis tests
"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.
• Aug 9th 2010, 02:11 PM
pickslides
Quote:

Originally Posted by sharpe

H0: theta = 0.5
H1: theta = 0.75

Should it not be

$H_0: \theta = 0.5$

$H_1: \theta > 0.5$

Quote:

Originally Posted by sharpe
and in each case give the type 1 and 2 error probabilities. Which test is preferred?"

For a type 1 error you are being asked to find the probability of rejecting $H_0$ given it is true.
• Aug 10th 2010, 11:55 AM
sharpe
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