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Math Help - type i and ii error

  1. #1
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    type i and ii error

    I have an exponential population. A single observation is used to test the null hypothesis that the mean waiting time is p = 10 against the alternative hypothesis that p does not equal 10. If null is rejected if and only if observed value is < 8 or > 12, find probability of type I error

    I'm clueless...any help is appreciated
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  2. #2
    MHF Contributor matheagle's Avatar
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    write down your density and what this p is.
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  3. #3
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    it doesn't specify a specific density. Also I was using p in place of theta. Sorry, I should have clarified.

    Don't I have to use the normal approximation to an exponential? And, if so, is this just the same equation as the normal approximation for Poisson?
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  4. #4
    MHF Contributor matheagle's Avatar
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    still
    some people write an exponential density as

    e^{-x/p}/p while others use pe^{-px}
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  5. #5
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    It's the latter one
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  6. #6
    MHF Contributor matheagle's Avatar
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    \alpha=\int_0^8f(x)dx+\int_{12}^{\infty}f(x)dx

    and I use the first density.
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  7. #7
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    Umpt

    Are you conversant with the concept of uniformly most powerful test?it works and i get it to be 1.0135
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