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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- Jun 13th 2009, 05:29 AMchrissy72finding 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

- Jun 13th 2009, 06:16 AMmatheagle
Since 80>30, the critical region is on the right.

With $\displaystyle \alpha=.05$ this becomes $\displaystyle (\chi^2_{.05},\infty)$.

You have 19 degrees of freedom IF you know and use $\displaystyle \mu$

otherwise you have 18 degrees of freedom IF you use $\displaystyle \bar X$.

It's in the box under... Statistical Hypothesis: Testing Variance -- Critical Region

In http://www.xycoon.com/ht_variance.htm