Power of a One-Sided Uniform Test
Let $X_1,\dots,X_4$ be independent and uniform on $[0,\theta]$. To test $H_0:\theta=1$ against $H_1:\theta<1$, reject $H_0$ when $\max_i X_i\le 1/2$. The size of this test is $1/16$. What is the power of the test when the true value is $\theta=3/4$? Give a reduced fraction.
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Source: Original problem written for AxiomIQ.