3. Let X1, ..., An denote an independent random sample from a population with a Poisson distribution with mean 2. Derive the most powerful test for testing Ho: 2 = 2 versus Ha : 2 = 1/3. 4. Three classes in elementary statistics are taught by three different persons: a regular faculty member, a graduate teaching assistant, and an adjunct from outside the university. At the end of the semester, each student is given a standardized test. Five students are randomly picked from each of these classes, and their scores are as shown in Table 9.3.2. Table 9.3.2 Faculty Teaching assistant Adjunct 93 88 86 61 90 56 87 76 73 75 82 90 92 58 47 (a) Construct an analysis-of-variance table and interpret your results. (b) Test at the 0.05 level whether there is a difference between the mean scores for the three persons teaching. Assume that the conditions of completely randomized design are met