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b) A large highway construction company owns a large fleet of lorries. The company wishes to compare the wearing qualities of two different types of tyres for use on its fleet of lorries. To make the comparison, one tyre of Type A and one of Type B were randomly assigned and mounted on the rear wheels of each of a sample of lorries. Each lorry was then operated for a specified distance and the amount of wear was recorded for each tyre. The results are shown in Table 1. Assuming that tyre Type B is more expensive than tyre Type A, estimate the 95% confidence interval for the difference between the means of the populations of the wear of the tyres and test the hypothesis that there is a significant difference between the two means at the 5% level. Comment on the choice of tyres. (Make any necessary assumptions). Lorry number Table 1 Results from the tyre wear 1 2 3 9.8 10.3 9.7 4 5 7 6 10.3 8.6 8.8 11.9 Wear of Type A tyres Wear of Type B 9.8 9.4 11.0 9.1 8.3 10.3 10.8 tyres (20 Marks)