8. Standard approach to build test We discuss population mean problem here. Usually, we use / to denote the unknown mean of a population. Given a hypothesis is not difficult. Null hyphothesis Alternative hypothesis Ho : H = Ho Ha : 14 / Ho Ha : / > Ho Ha : H S HO (a) Suppose we have test statistics, T, and the problem becomes how can we identify R.R. in order to achieve given significant level o* and minimize the probability of type II error, B. Please show and explain why we can reduce the problem to Pr(T E R.R.| u = HO) Sax. (b) We can furthermore reduce above formula to Pr(T E R.R. | p = HO) = a*. Please explain why we can only consider the equal case. (Consider the trade off between a and B.) (c) Customarily, the R.R. are choosen as the following format: Alternative hypothesis R.R. Corresponding formula Ha : H # Ho Ha : p 2 Ho Tz c Pr(T 2 c | p =Ho) = 0* Ha : H C Ho T