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Thread: finding a critical region

  1. #1
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    finding a critical region

    Let X1,X2,....X19 be a random sample of size n=19 from the normal distribution N(mu,sigma^2). How do you find a critical region, C, of size alpha=0.05 for testing H0: sigma^2=30 against H1: sigma^2=80? Thankyou
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  2. #2
    MHF Contributor matheagle's Avatar
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    Since 80>30, the critical region is on the right.
    With \alpha=.05 this becomes (\chi^2_{.05},\infty).
    You have 19 degrees of freedom IF you know and use \mu
    otherwise you have 18 degrees of freedom IF you use \bar X.

    It's in the box under... Statistical Hypothesis: Testing Variance -- Critical Region
    In http://www.xycoon.com/ht_variance.htm
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