2. Eleven tires were each measured for treadwear by two methods, one based on weight and the other on groove wear. The following are the data, in thousands of miles. Weight method ( Groove method ( Difference " , ) H, ) 30.5 28.7 1.8 30.9 25.9 5 31.9 23.3 8.6 30.4 23.1 7.3 27.3 23.7 3.6 20.4 20.9 -0.5 24.5 16.1 8.4 20.9 19.9 T 18.9 15.2 3.7 13.7 1.5 2.2 11.4 11.2 0.2 X =23.71 X, =19.95 s =7.19 S =5.77 d=3.75 , s =3.22 The data are provided in the data file A5_Treadwear_Q3.xisx. (a) Use the proper graphical tools in R and R commander to assess whether it is reasonable to apply the procedure you chose in Question 3. (b) of Part A. Make sure to write down the assumptions of the procedure and address whether every assumption is satisfied. (5 marks) (b) Use R commander to determine if there is sufficient evidence at the 5% significance level to conclude that, on average, the two measurement methods give different results? Make sure to include all the six components of a hypothesis test. Compare the answer with the one you obtained by hand in Question 3. (b) of Part A. (5 marks) (c) Obtain and interpret a 95% two-sided confidence interval for the mean difference between measurements from the weight and groove methods. Compare this interval to the one you calculated by hand in Question 3. (d) of Part A. (2 marks) 3. An American roulette wheel contains 18 red numbers, 18 black numbers, and 2 green numbers. The following table shows the frequency with which the ball landed on each colour in 300 trials. At the 5% significance level, do the data suggest that the wheel is out of balance? Number Red Black Green