Manual solutions please :)a) (10 marks)Do these data provide sufficient information to indicate at the 5% significance level that the new bumper reduces the variance of vehicle downtime? Briefly discuss the steps of the test you perform showing all relevant details.(b) (10 marks)Do these data provide sufficient information to indicate at the 5% significance level that the new bumper reduces mean vehicle downtime? Briefly discuss the steps of the test you perform showing all relevant details.(c) (6 marks)What are the requirements of the hypothesis tests you performed in parts (a) and (b)? Are the requirements about the experimental design, the variable of interest and the measurement scale met? Explain your answers.

Exercise 1 {26 marks = 10 + 10 + 6) The management of a large eet of vehicles is concerned about vehicle downtime, i.e., about the number of days a vehicle is unavailable due to some repair after an accident, and decided to experiment with a new bumper that might reduce the damage in low-speed collisions. In order to see whether this new bumper is indeed effective, she took a random sample of the company's cars and had the new bumper installed on them for a trial period of two months. At the end of the trial period, accident data showed that the cars with the new bumper had 12 repair incidents, while during the same period another random sample of cars equipped with the original bumper had 9 repair incidents. Vehicle downtime due to these repair incidents are shown in the following table. New Original 9 7 2 5 5 7 12 4 5 13 4 4 7 S 5 14 11 13 3 7 In this table New and Originaf denote vehicle downtime in number of days per repair incident for cars with the new bumper and with the original bumper, respectively. Using this data set perform the following tasks. Do all calculations 'manually' (i.e., with a hand calculator without using R, Excel, or any other software), showing the relevant formulas and the major steps