(b) Tests were made to determine the performance of cars in kilometres per litre of petrol using two additives. Eighteen new vehicles of the same type took part, nine using additive 1, and the other 9 using additive 2. The average distance covered by each car per litre is given in the table below. You are given that the average distances are normally distributed. Additive 1 12.3 17.3 15.5 13.7 11.9 10 14.6 12.8 16.4 Additive 2 18.4 14.8 16.6 12 13.9 15.7 17.5 16.3 14.3 (i) State an appropriate pivotal quantity for estimating, the ratio of the population variances. (ii) Derive a 100(1-a) % confidence interval for, the ratio of the population variances. (iii) Construct a 99% confidence interval for, the ratio of the population variances.

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