Read through the attachments below and address all the questions as guided appropriately.

(i) An analysis using the bivariate correlation model resulted in a sample correlation coefficient of r =0.8 based on a sample of 20 data pairs. Test whether the population correlation coefficient, p, is greater than 0.5. [3] (ii) A sample of 10 pairs of values from a different bivariate normal distribution resulted in a sample correlation coefficient of r = 0.62 . Obtain a 95% confidence interval for the underlying population correlation coefficient. [3] [Total 6]A life insurance company issues five-year without profit endowment assurances for an annual premium of $3,600 and a sum assured of $20,000 payable on maturity or at the end of the year of death if earlier. The company uses the following assumptions for profit testing: Year Mortality Surrender Expenses at Reserves at Surrender rate rate start year per end of year value at end policy per policy of year per policy 0.01 0.05 $750 $3,100 $2,800 2 0.01 0.05 615 $6,800 E6.250 3 0.01 0.05 E15 $10,900 $10,000 0.01 0.05 $15 $15,300 $14,500 0.01 0 E15 Surrenders occur only at the end of a year immediately before a premium is paid. The surrender rates shown in the table above are applied to the number of policies in force at each year-end. (i) Set out the column headings and the formulae you would use to calculate the profit arising each year per policy in force at the beginning of the year. [8] (ii) Calculate (to the nearest 1%) the internal rate of return obtained by the company. Basis: Interest 6% pa [13] [Total 21]