(a) Chose an a; and then (b)define the rejection region in terms some statistic T(x) The latter is necessary to enable us to determine e via some known distribution This is the distribution of the test statistic T(x)under Ho(i.e. when Ho is true The next question which naturally arise is: What do we need the probability of type Ii error B for? The answer is that we need b to decide whether the test defined in terms of Cl(of course Co) is a'good'or a ' test. As we mentioned t the outset, the way we decided to solve the problem of the trade-off between a and B was to choose a given small value of a and define C1 so as to minimize 6. At this stage we do not know whether the test defined above is a 'good'test or not. Let us consider setting up the apparatus to enable us to consider the question of optimality(a) Chose an α; and then (b) define the rejection region in terms some statistic τ (x). The latter is necessary to enable us to determine ε via some known distribution. This is the distribution of the test statistic τ (x) under H0 (i.e. when H0 is true). The next question which naturally arise is: ”What do we need the probability of type II error β for ?” The answer is that we need β to decide whether the test defined in terms of C1(of course C0) is a ’good’ or a ’bad’ test. As we mentioned at the outset, the way we decided to solve the problem of the trade-off between α and β was to choose a given small value of α and define C1 so as to minimize β. At this stage we do not know whether the test defined above is a ’good’ test or not. Let us consider setting up the apparatus to enable us to consider the question of optimality. 6