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Finding a Uniformily Most Powerful Region

  1. Mar 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Let [tex]X_1,...,X_{25}[/tex] be from a sample of 25 from a normal distribution [tex]N(\theta,100)[/tex]. Find a UMP region with [tex]\alpha = 0.1[/tex] for testing [tex]H_0:\theta=75 \ VS \ H_1:\theta>75[/tex]

    2. Relevant equations

    3. The attempt at a solution

    So after performing the Likelihood ratio test, I determined the critial region to be [tex](\Sigma X_i => K)[/tex] where K is some constant.

    Using the CLT [tex]\frac{\Sigma X_i - n\mu}{\sigma \sqrt{n}}[/tex]

    [tex]P(\Sigma X_i => K) =P_{H_0}( \frac{\Sigma X_i - 25(75)}{10\sqrt{75}} => \frac{K - 25(75)}{10\sqrt{75}} )=0.1[/tex]

    [tex]\frac{K - 1875}{86.6}=1.28[/tex] solving for K = 1985.848

    Have I made a mistake anywhere?
  2. jcsd
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