5.12 From experience it is known that a certain brand of tyre lasts, on average, 15 000 miles with standard deviation 1250. A new compound is tried and a sample of 120 tyres yields an average life of 15 150 miles. Are the new tyres an improvement? Use the 5% significance level. 5.13 Test H0: π = 0.5 against H0: π ≠ 0.5 using p = 0.45 from a sample of size n = 35. 5.14 Test the hypothesis that 10% of your class or lecture group are left-handed.

5.15 Given the following data from two independent samples X1 = 115 X2 = 105 s1 = 21 s2 = 23 n1 = 49 n2 = 63 test the hypothesis of no difference between the population means against the alternative that the mean of population 1 is greater than the mean of population 2. 5.16 A transport company wants to compare the fuel efficiencies of the two types of lorry it operates. It obtains data from samples of the two types of lorry, with the following results: Type Average mpg Std devn Sample size A 31.0 7.6 33 B 32.2 5.8 40 Test the hypothesis that there is no difference in fuel efficiency, using the 99% confidence level.