Question 1 a) The following data table records 200 observations on co-movements between interest rates and stock market indices. Total Interest rate decline 12 88 Stock price decline Stock price increase Interest rate increase 75 25 100 87 113 200 Total 100 i. Denote an increase in the stock market index by SI, a decline in the stock market index as SD, an increase in interest rates by II, and a decline in interest rates by ID. Using the data in the table above, compute the respective probabilities in this table. [2 marks] Interest rate Interest rate Total decline increase Stock price decline Pr(SD and ID) Pr(SD and 11) Pr(SD) Stock price increase Pr(Si and ID) Pr(SI and II) Pr(SI) Total Pr(ID) Pr(1) ii. What is the probability of a decline in the stock market change, if there is an increase in interest rates? (10 Marks) 1.000 iii. What is the probability of an increase in the stock market, if interest rates decline? [10 Marks] b) A sample is conducted to estimate the gender pay differences in the city of Portsmouth. A survey of 100 men found an average wage of £26,500 with standard deviation £3,000. A sample of 200 women found an average wage of 1 £22,300 with standard deviation £2,500. Test whether the wage gap between men and women is statistically significant or not at 95% level of confidence. The critical value is 2a/2 = 1.96.