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4. Let $X_{1},…X_{n}$ be $iid$ observations with median $?$ and suppose a sample of size $n=30$ is collected. Consider testing $H_{0}:??0versusH_{1}:?>0$
(a) Find the size $?$ of the test that rejects the null hypothesis if $#{X_{i}>0}?19$ (b) Determine the power of the test in $(a)$ if, in fact, $X_{i}?iidN(?=0.5,?_{2}=1)$. (c) Consider a test that rejects $H_{0}$ if $X?>n???z_{?}$. Using the size $?$ found in part (a), compare the power of this test with the test in part $(a)$, in fact, $X_{i}?iidN(?=$ $0.5,?_{2}=1)$