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Math Help - Basic power function

  1. #1
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    Basic power function

    I'm trying to re-learn statistics but the terminology used in my class is different than what I'm used to. Can somebody tell me if I'm on the right track?


    Suppose units per day X has a normal distribution with unknown mean \theta and standard deviation \sigma=8.

    I want to test H_0:\theta \ge 100 vs. H_1:\,\theta < 100.


    Suppose n=64 days and H_0 will be rejected if the sample mean daily units satisfies \bar{x}<98. What is the value of the power function if \theta=99 ?

    My work:

    P( \bar{x} >97)=P \left( Z> \frac{99-97}{8/ \sqrt{64}} \right) =P(Z=2)=0.0228

    So,

    1-0.0228= \bf{0.9772}

    Am I understanding this "power function" thing correctly?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Sorry, you reject the null for \bar X<98

    P( \bar X<98)=P \left( Z< \frac{98-99}{8/ \sqrt{64}} \right) =P(Z<-1)
    Last edited by matheagle; February 5th 2010 at 03:24 PM.
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  3. #3
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    I know its basic, but I'm still trying to get my head around this.

    So does that mean the value of the power function is 0.1587 and the probabilty of a type 2 error is 0.8413?
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