AGSC 5060: Statistics for Research Page 4 of 8 Question 4. A tire manufacturer wanted to compare the wearing qualities of two different types of tires, A and B. Six cars of similar weight and design were randomly chosen for the experiment. For each car, a tire of type A and a tire of type B were randomly selected and placed on the rear wheels. Each car has both type A and type B tires in its rear wheel. The cars were then operated for 5000 miles over similar terrain under similar driving conditions and the amount of tread wear (in thousandths of an inch) was recorded, with the following results (10 marks): Tire Cars Sample Statistics 1 2 3 4 5 6 S Tire A 10.7 9.8 11.3 9.5 8.6 9.4 9.883 0.970 Tire B 10.3 9.4 11.5 9.0 8.2 9.0 9.567 1.167 Difference 0.4 0.4 -0.2 0.5 0.4 0.4 0.317 0.256 (Tire A - Tire B) (i) Using 5 percent significance level, test whether there is a difference between average tread wear for tires A and B. What statistical test would you choose (assume that the difference scores are normally distributed)? As part of hypothesis testing, state null and alternate hypotheses, calculate test statistics, make decision and draw a meaningful conclusion. (8 marks) rks) (ii) Based on your decision in (i), if you were the customer, would you have any preference of buying one over other? If yes, which one would you buy? (note: data given above are amount of tread wear when a car is driven 5000 miles, i.e. less tread wear is better as the tire lasts longer) (2 marks)