7. Which test is better? Any function of sample can be test statistics and any subset of support of selected test statistic can be R.R.. Then the intuitive question is which one is better? (a) Any hypothesis test will give us four possible outcomes, because we have two possible truth and two possible conclusions. Please draw a 2 x 2 table as we shown in class to indicate these four possible outcomes. Futhermore, which of them are correct and which of them are incorrect outcomes? For the incorrect outcomes, please also show the name of different kind of errors in the table. (b) Show the definitions of a, B and power. (c) Consider the fair coin example in class. The hypothesis is given as Ho : p = 0.5 and Ha : p # 0.5, where p is the probability of "head". Then, test statistic is given as T, the number of head in 10 flips. Then, it is reasonable to assume T follows a binomial distribution with parameters, n = 10 and p, i.e. Bin(10, p). Now, I claim two R.R.s as: R.R.1 = {7, 8, 9, 10} and R.R.2 = {9, 10}. 1. Calculate o and B with respect to R.R.1. 3 2. Calcualte o and 8 with respect to R.R.2. 3. Compare the change of o and B and draw the conclusion of trade-off between o and B. 4. We want to minimize both a and S, which means we have to find a balance point between them. Explain the standard stratege we use here in language