(a) Suppose that X1,...,Xn are an i.i.d. random sample of size n= 15 drawn from a Normal distribution with unknown meanand known variance ^2= 4. Using python, plot the power of the test H0: = 0 versus Ha:6= 0 as the true mean varies at level = 0.05

(b) Then using the same information from part (a) except for fixing at = 3, plot the power of the test as varies.

(c) Fix back to = 0.05 and plot the power of the test as n varies.

(d) Fix n back to n= 15 and plot the power of the test as ^2 varies.