Provide step by step answers to the following economics questions.

A general insurance company is debating introducing a new screening programme to reduce the claim amounts that it needs to pay out. The programme consists of a much more detailed application form that takes longer for the new client department to process. The screening is applied to a test group of clients as a trial whilst other clients continue to fill in the old application form. It can be assumed that claim payments follow a normal distribution. The claim payments data for samples of the two groups of clients are (in f100 per year): Without screening 24.5 21.7 35.2 15.9 23.7 34.2 29.3 21.1 | 23.5 28.3 With screening 22.4 21.2 36.3 15.7 21.5 7.3 12.8 21.2 23.9 18.4 (i) (a) Find a 95% confidence interval for the difference between the mean claim amounts. (b) Comment on your answer. [6] (ii) (a) Find a 95% confidence interval for the ratio of the population variances. (b) Hence, comment on the assumption of equal variances required in part (i). [4] (iii) Assume that the sample sizes taken from the clients with and without screening are always equal to keep processing easy. Calculate the minimum sample size so that the width of a 95% confidence interval for the difference between mean claim amounts is less than 10, assuming that the samples have the same variances as in part (i). [3] [Total 13](i) Define the accumulation factor A(t,/+h) and give a formula for the force of interest o () per unit time in terms of the accumulation factor. [2] (ii) The force of interest 6() at time ? (measured in years) is given by 5(1) =0.01/ +0.04. (a) Calculate the corresponding nominal rate of interest for the period / = 1 to / = 2. (b) If an investment of 1 is made at time /= -, calculate the value to which it will have accumulated by time / =6. [6] (iii) Calculate the accumulated value after 6 months of an investment of $100 at time 0 at the following rates of interest: (a) a force of interest of 0.05 pa (b) a rate of interest of 5% pa convertible monthly (c) an effective rate of interest of 5% pa. [3] [Total 1 1]