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Testing Hypotheses Binomial

  1. May 6, 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).

    I am completely lost with how to even start this problem. Any help would be awesome.
  2. jcsd
  3. May 7, 2013 #2


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    Science Advisor

    Hey LBJking123.

    First try calculating the value of H0 by finding the probabilities corresponding to theta = 0.5

    A hint for this is to get the estimator distribution for theta. You are assuming that X is binomial (5,theta/5), so you need to get the mean and use that as an estimator for theta.

    After this you have to use a test to get your final statistic and this can range from using the binomial distribution directly to using something like a likelihood ratio statistic.

    What techniques have you covered in class?
  4. May 9, 2013 #3
    Thanks chiro!
    We have covered both of those methods (binomial and likelihood ratio statistic), but I think we are supposed to use the binomial to do this one.
    This is what I have so far (I am not very confident):

    Sample average = 1.75


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

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

    It just seems like I am totally missing something....

    The mean on the binomial(5,theta/5) is just theta. I don't understand how that helps though.
    Last edited: May 9, 2013
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