This question has 3 parts. The research department of a manufacturer of high-performance road bike tyres has developed a new rubber compound that they believe will result in tyres that have a population mean lifetime, UN (measured in miles), that is greater than the population mean lifetime, Mc, of tyres using the rubber compound currently available. The research department has been informed by management that the change to the new rubber will only be made if there is significant evidence that the difference in the mean lifetimes of the tyre exceeds 400 miles. i) What would be the appropriate null and alternative hypotheses to test this claim? O Ho : UN - MC 2 400; Ha : MN - MC 400 O Ho : UN - MC 400ii) A sample of tyres using each type of rubber is selected and the following sample mean lifetimes and sample standard deviations were determined: :EN :1?13 miles, 3N : 25 miles, nN : 32 g 2 1300 miles, so = 15 miles, ng = 32 The value of the appropriate test statistic is: O 50.76 0 1.76 O 2.12 O 5.30 O 2.52 iii) What is the smallest significance level from the following at which you would conclude that the population mean lifetimes differ by more than 400 miles? (Hint: the degrees of freedom is 50) O a = 0.05 O a = 0.005 O a =0.1 O a = 0.01