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Math Help - Hypothesis Testing

  1. #1
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    Hypothesis Testing

    Let X_{1}, ... , X_{n} be a random sample from an exponential distribution with mean \theta. Show that the likelihood ratio test of H_{0} : \theta = \theta_{0} against H_{1} : \theta = \theta_{1} has a critical region of the form \sum^{n}_{i=1} x_{i} \leq c_{1} or \sum^{n}_{i=1} x_{i} \geq c_{2}. How would you modify this so that chi-square tables could be easily used?
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  2. #2
    MHF Contributor matheagle's Avatar
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    The sum of indep EXP(theta's) is a \Gamma(n,\theta)

    Call this sum of X_i's X and now transform to the chi square

    A \chi^2_a=\Gamma(a/2,2)

    So do some calculus one with the substitution x/\theta=y/2
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