(1) What test would you use in each of the following contexts? (a) The data below shows the student performance under high and low temperature. You want to know if the performance changes significantly when you move from high to low temperatures. (0.5 Points) High Low Person Temperature Temperature 18 15 12 14 17 15 14 12 UI A 16 16 11 9 14 14 8 17 16 9 18 14 10 15 17 11 12 11 12 19 18 (b) compare if two distributions are the same. (0.5 Points) (c) The data below shows the student performance under red, blue and green light. You would like to know which color results in best performance (0.5 Points) Red Green Blue Person Light Light Light 25 42 55 22 39 45 31 32 42 35 30 51 27 39 46 (d) A random sample of 30 employees from the Sales department and another 36 employees from the Marketing department were selected and were administered an aptitude test. You want to know if there is a significant difference between their scores. (0.5 Points)(2) The average annual returns (in percentages) on Brown Small Cap Index Fund (BCSIX) and S&P 500 for the past 10 years are given below: BCSIX S&P 500 29.22 31.29 -0.67 -4.45 28.9 21.69 8.34 11.80 8.75 1.34 2.19 13.53 48.98 32.21 17.47 15.84 0.11 2.06 22.56 14.3 Does BCSIX perform significantly better than S&P 500? Please perform all the steps in hypothesis testing (3 Points)