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Math Help - need help to construct UMPT (uniformly most powerful test)

  1. #16
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    EDIT: Whoops
    Last edited by theodds; February 23rd 2011 at 06:22 AM. Reason: Misread Question
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  2. #17
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    Quote Originally Posted by Volga View Post
    Would you mind showing how one would approach the second part of the question, viz "Suppose n=10, sample mean is 2.42, and =1.5. Will you reject Ho at a significance level of 5%?" I am still hoping to have this completed as this is a good practice question for the exam. I promise never to attempt constructing a UMPT in real life after I am done with this Stat Inference exam )))
    How can the sample mean be 2.42? That implies \sum X_i = 24.2 which is impossible.

    Anyways, P_{\lambda = 1.5} (\sum X_i > 24.2) = .01

    so yes, you would. I used R to calculate the probability, since it's a tedious calculation to do exactly (essentially summing the pmf). In other words, the appropriate k that gives the size of desired test is less than 24.2.

    I don't worry about you having to calculate UMP tests in real life because, in general, they don't exist Even throwing in a single nuisance parameter is typically going to ruin things for you, so most of the tests that people use in practice aren't UMP.
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  3. #18
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    I used R to calculate the probability
    what's that?

    Because, I wouldn't know how to calculate P_{\lambda = 1.5} (\sum X_i > 24.2).
    Last edited by Volga; February 23rd 2011 at 03:18 PM.
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  4. #19
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    Quote Originally Posted by Volga View Post
    what's that?

    Because, I wouldn't know how to calculate P_{\lambda = 1.5} (\sum X_i > 24.2).
    R is (free) software. Explicitly you calculate it as

    <br />
P(\sum X_i > 24.2) = 1 - P(\sum X_i \le 24.2) = 1 - \sum_{x = 0}^{24} \frac{15^x e^{-15}}{x!}<br />

    because \sum X_i is Poisson(15) when \lambda = 1.5.
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  5. #20
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    Oh I see! I thought "R" was some approximation formula )))
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