Suppose that X1,. . . , Xn is an m.a. of a distribution U (0, θ]....

Suppose that X1,. . . , Xn is an m.a. of a distribution U (0, θ].

(a) Find the most powerful test of size α to test H0: θ = θ0 vs Ha:

θ = θa, where θa <θ0.

(b) Is the test obtained in part (a) the UMP (α) to test H0: θ = θ0 vs Ha:

θ <θ0 ?.

(c) Find the most powerful test of size α to test H0: θ = θ0 vs Ha: θ =

θa, where θa> θ0.

(d) Is the test obtained in part (c) the UMP (α) to test H0: θ = θ0 vs Ha:

θ> θ0 ?.

(e) Are the most powerful tests of size α found in (a) and (c) unique?

Expert Solution

orchestra answered 1 year ago

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