Thread: testing hypothesis, alpha and beta

1. testing hypothesis, alpha and beta

Supposes a random sample X1,...Xn is drawn from a uniform distribution on the interval [0,theta].
H0: theta=1
H1: theta=2
Find the minimum value of beta that can be attained among all test procedures for which alpha=0

I know the answer is (1/2)^n so I am trying to work backwards to solve this but am still having some troubles. Beta is equal to the probability of not rejecting the null when the alternative is true, or P(X<1 given Theta=2). Just not sure what value X needs to be? Did I do this right? Thanks!

2. what did you get for your test statistic?
Did you take the ratio of the two likelihood functions?