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Testing Hypotheses with Bernoulli Distribution

  1. Apr 12, 2013 #1
    This is the question:
    Suppose that X1......Xn form a random sample from the Bernoulli Distribution with unknown parameter P. Let Po and P1 be specified values such that 0<P1<Po<1, and suppose that is desired to test the following simple hypotheses: Ho: P=Po, H1: P=P1.
    A. Show that a test procedure for which α(δ) + β(δ) is a minimum rejects Ho when Xbar < c.
    B. Find the value of c.

    I know that this problem is not that difficult I just can't figure out where to start. I know the Bernoulli distribution, but I can't figure out how to get α(δ) and β(δ). I have not seen any problems like this so I am kinda lost, any help would be much appreciated. Thanks!
  2. jcsd
  3. Apr 15, 2013 #2

    Stephen Tashi

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    Science Advisor

    You didn't say what [itex] \delta
    [/itex] is.
  4. Apr 15, 2013 #3


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    ƩX ~ Binomial (n,p0) under null hyp (H). You know the probabilities of X=0,1, ...,n under H. Find the value of X (= c, say) such that P[X≤c-1] < α ≤ P[X≤c]. Now compare your observed value of X with c.
    If you want a test of exact size α, then a randomized test is to be done.
    For large n you can use normal approximation due to De Moivre Laplace limit theorem.
    Last edited: Apr 15, 2013
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