Suppose that a single observation X is to be taken from the uniform distribution on the interval

Question:

Suppose that a single observation X is to be taken from the uniform on the interval [θ – 1/2, θ + ½], and suppose that the following hypotheses are to be tested:
H0: θ ≤ 3,
H1: θ ≥ 4.
Construct a test procedure δ for which the power function has the following values: π(θ|δ) = 0 for θ ≤ 3 and π(θ|δ) = 1 for θ ≥ 4.
Distribution
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