Assume that X1, ...,Xn is a random sample from the N(0, 2) distribution. For testing hypothesis H0 : = 2 0 against the alternative

Assume that X1, ...,Xn is a random sample from the N(0, σ2) distribution. For testing hypothesis H0 : σ = σ2 0 against the alternative H1 : σ2

= σ2 0 at significance level

α, find an unbiased test with a critical region of the form “reject H0 if n i=1 X2 i /σ2 0 <

C1 or n i=1 X2 i /σ2 0 > C2.”