The 2022 Formula One Technical Regulations issued by the International Automobile Federation (FIA) have allowed for plenty of design freedom. As the aerodynamicist of the Haas Formula One Racing Team, you are responsible for the choice of the sidepod solutions between two opposing airflow management philosophies - minimised sidepods versus maximised sidepods. All else unchanged, two versions of the new car one with minimised sidepods design and one with maximised sidepods design were built and tested.

Let min and max be the mean lap times (in seconds) of the new cars with minimised sidepods and maximised sidepods respectively. Track data of a random sample of 26 lap times were taken for both versions of the car during the winter testing of the 2022 season. It is claimed that the lap times are different between the car with minimised sidepods and maximised sidepods. The data is stored in the file time.txt. Assuming that lap times are independent, complete the exercises below.

In time.txt

min_sidepods max_sidepods 1 66.88 85.45 2 62.88 80.79 3 64.7 60.06 4 87.43 62.94 5 74.78 78.72 6 78.06 76.77 7 75.19 77.56 8 76.55 51.52 9 72.6 73.91 10 71.69 60.83 11 70.8 74.77 12 77.34 69.34 13 74.57 75.15 14 77.32 73.23 15 70.78 89.01 16 56.83 62.94 17 65.21 75.81 18 73.7 58.47 19 72.96 67.24 20 75.05 66.17 21 73.78 75.05 22 64.24 64.29 23 64.2 72.17 24 69.2 72.91 25 70.77 70.17 26 71.6 60.07

Can u make code for R studio for calculate those question

Compute the absolute value of the test statistic for this hypothesis test.

Compute the P-Value for this hypothesis test.

Compute the length of a two-sided 95% CI for, minmax, the difference in lap times of a car with minimised sidepods and maximised sidepods. (Hint: The length is the upper confidence limit minus the lower confidence limit.)

Compute the length of a two-sided 90% CI for, minmax, the difference in lap times of a car with minimised sidepods and maximised sidepods. (Hint: The length is the upper confidence limit minus the lower confidence limit.)