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Math Help - Hypothesis tests

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by sharpe View Post

    H0: theta = 0.5
    H1: theta = 0.75
    Was this given to you?

    Should it not be

    H_0: \theta = 0.5

    H_1: \theta > 0.5



    Quote Originally Posted by sharpe View Post
    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.
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  3. #3
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    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
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