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
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