Question

The following review problem is on hypothesis testing. Could you please guide on how to approach this?

Suppose one can observe X₁, X₂, · · · , X_n, which are i.i.d observations from a Uniform(0, θ) distribution. For θ₀ > 0, we want to test:

H₀ : θ = θ₀ vs H₁ : θ > θ₀.

Use the test statistic T_n = X(n)/ θ₀ to perform a α-level test, where X(n) = max{X₁, X₂, · · · , X_n}.

(a) When should one reject H₀ in favor of H₁?

(b) For any θ₁ > 0, compute the power of the test at θ = θ₁.

Answer 1