5. (Hypothesis testing) In the same setting of problem 4, the gambling company wants to do some hypothesis testing based on the survey's results. (a) (10') Suppose out of the n draws, there are ni(i=1,2,3) that supports Alice, Bob and Cathy respectively. Conduct a level likelihood ratio test for the following hypothesis: Null: =0=(01,02,03). Alternative: =0. (b) (10) Suppose one wants to test whether location (if the person lives in city or country) is independent of the support rate. Let's look at the following more fine-grained survey sampling result: Conduct the homogeneous test: Null: location category has no effect on support rate: 1j=2j,j= 1,2,3. Alternative: otherwise