Question 5 {1H marks] Let X; and K- be the annual investment returns of Hedge Fund A and Hedge Fund B in Year 1'. respectively: for i = 1, . . . ,5. Suppose you are a data analytics oonsultant of a fund of hedge funds and are asked by your client to analyse the performances of Hedge Fund :1 and Hedge Fund B. The following table gives the data on the annual returns of the two hedge funds from 1fear 1 to Year 5. After studying the past performanoes of the two hedge funds. you believe that the annual returns of each of the two funds follow a. Normal distribution. Furthermore. suppose that the annual returns of the two funds are independent. and that the annual returns of each of the two funds in different years are independent. The population means n}; and lay of the annual returns of the two funds are unknown. It is given that the population standard deviations J; and try of the annual returns of the two funds are {12' and {13. respectively. Suppose that the population means and population varianoes of the annual returns of the two funds remain unchanged over the five years. Using the above assumptions and given data. answer the questions in Part a] - Part e] as follows: a] Find a 95% symmetric oondence interval for the difference in the population means For - y. {4 marks] b) Based on the result in Part a), comment on whether there is evidence to suggest a difference between the expected annual returns of the two funds. (1 mark) Now, based on the above assumptions and given data, you would like to test whether there is evidence that the expected annual return of Hedge Fund A exceeds the expected annual return of Hedge Fund B. c) State the null hypothesis Ho and the alternative hypothesis H1. (1 mark) d) Determine the standardised test statistic for the data, and also clearly state its distribution under Ho- (2 marks) e) Should Ho be retained or rejected at a 1% significance level? Justify your answer. (2 marks)