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Test Hypotheses with sample of Binomial RV's

  1. May 9, 2013 #1
    Hi, I am trying to teach myself how to test hypotheses for any distribution, but am having some trouble.

    X=number chosen each year
    θ=Mean number chosen in the population

    H0: θ=.5
    h1: θ>.5

    The random sample of n=4 is 0,1,3,3

    Test the Hypotheses at α≤0.05 assuming X is a binomial(5,θ/5).

    This is what I have so far, but I feel I am completely missing something..

    Sample average (Xbar = 1.75


    Reject H0 if P(Xbar≥1.75, given that X is binomial(5,.1)) ≤ 0.05

    Then I figure out 1-P(Xbar≤1.75)=0.08146 which is greater than 0.05 so I reject the null.

    I know something is not right... Any help would be much appreciated. Thanks!
  2. jcsd
  3. May 10, 2013 #2


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  4. May 10, 2013 #3
    So would I want to do a z score, like on page three of that document? That seems like it would work better.

    Then, I get P(Z≥(1.75-.5)/SQRT(.25/4))=P(Z≥5)=0, which is less than 0.05 so I reject the null..?
  5. May 10, 2013 #4


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    If that distribution and region corresponds to H0 then yes you reject the null.

    Remember that a p-value is looking at a probability for some estimator distribution that relates to a hypothesis.
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