Question 1 (25 marks)

Below are the quarterly returns on investment (in 000s) of two different investment projects which had the same initial outlay. There is a sample of 16 quarters of returns and your manager has asked you to investigate the relative performance of each project. In particular, your manager suspects that 'Investment B' outperforms 'Investment A' and she would like you to test this hypothesis.

1. Calculate the mean return and the variance of each project.

[10 marks]

1. Perform an appropriate statistical test that incorporates your manager's hypothesis and discuss the result.

[15 marks]

Hint: in this question, assume that both returns come from independent samples, are both normally distributed and that the true (but unknown) variances are the same.

Quarter Project A Project B 201801 85 83 201802 85 82 201803 87 86 201804 91 89 201901 95 92 201902 99 98 201903 96 101 201904 98 104 202001 95 100 202002 91 99 202003 92 99 202004 96 102 202101 99 104 202102 100 106 202103 99 99 202104 101 105