Question: Let X1, X2, , X10 be a random sample from a distribution with the p.d.f. f(x) = 1 e x/, x > 0, > 0.

Let X1, X2, , X10 be a random sample from a distribution with the p.d.f. f(x) = 1 e x/, x > 0, > 0.

Consider the following hypothesis test: H0 : = 0.5 vs. H1 : = 1

Fix a significance level = 0.01. Design the critical regions

(a) C1 = X(1) > c1 ,

(b) C2 = X(10) > c2 .

Which critical region is more powerful?

3. Let X1, X2, . .. , X10 be a random sample from a distribution with the p.d.f. f (ac) = -e-210, x> 0, 0>0. Consider the following hypothesis test: Ho : 0 =0.5 vs. H1 : 0 =1 Fix a significance level a = 0.01. Design the critical regions (a) C1 = {X(1) > ci}, (b) C2 = {X(10) > C2} . Which critical region is more powerful

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