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2. (30 points) The following sample of size n = 100 involves 3 different blood types, Type A, B and C. In the sample 30 have Type A, 33 have Type B and 37 have Type C. Consider a multinomial distribution, where the probability of Type A is 8, Type B is 1 - 20 and Type C is 0 where 0 0 5 7. (a) (10 points) Find the maximum likelihood estimator for d. (b) (10 points) Perform a goodness of fit test for the above model with tests of size a = 0.005 and o = 0.01. (c) (10 points) Now assume the above model is true and perform a hypothesis test: Ho : 0 = versus the alternative #, : 0 # 2. Find the form of the generalized likelihood ratio test acceptance region and determine whether you would accept or reject the null hypothesis when o = 0.005 and o = 0.01