One-Sided Test (35 points) Suppose you get data on returns, with denoting the return at time , where = 1, ... , . A number like = 0.01 indicates a 1% return. You are willing to assume that iid (, 0.12 ), that is, that returns are independent of each other, and are all normally distributed with an unknown mean and a known standard deviation of 10% (0.1). For your data, you obtain 15 past returns ( = 15), and see a sample average of only 2%: = 1 15 15 =1 = 0.02 You wish to show that is below 8% = 0.08 (a number on the lower end of average stock returns since the 1950s) to conclude that this financial instrument has poor performance. (a) (5 points) Write the null and alternative hypotheses for this test. (b) (5 points) We will use the sample average ( ) as the test statistic. Explain briefly why lower values (smaller means) are stronger evidence against the null. Keep your answer short and simple. (c) (5 points) What is the distribution of = 15 1 15 =1 ? Leave your answer as a function of . (d)