(Solved): 4. Let X1,Xn be iid observations with median and suppose a sample of size n=30 is coll ...

4. Let $X_1,\dots X_n$ be $iid$ observations with median $?$ and suppose a sample of size $n=30$ is collected. Consider testing $H_0:??0\text{ versus }{H}_1:?>0$ (a) Find the size $?$ of the test that rejects the null hypothesis if $\#\left\{X_i>0\right\}?19$ (b) Determine the power of the test in $(a)$ if, in fact, $X_i\stackrel{iid}{?}N\left(?=0.5,{?}^2=1\right)$. (c) Consider a test that rejects $H_0$ if $\stackrel{?}{X}>\frac{?}{\sqrt{n}}{z}_{?}$. Using the size $?$ found in part (a), compare the power of this test with the test in part $(\mathrm{a})$, in fact, $X_i\stackrel{iid}{?}N(?=$ $0.5,{?}^2=1)$