An HR manager at a large agricultural equipment company is considering proposingputting the sales staff on 4 day 10 hours/day work weeks, instead of their current 5day 8 hours/day week. It is believed that this will decrease the amount of drivingthey must do during a typical work week. They put 16 of their sales people on the 4day week for one month, then on the 5 day week for one month, and have themrecord their driving distances. The data is recorded in the DrivingDistance dataset.Assume that all conditions for valid tests are met.

4-Day Week 2912 6112 6175 1102 3279 4997 1690 6606 1060 6392 3362 5555 1130 5771 8325 2376

5-Day Week 2798 7734 7505 844 4592 8117 1228 8728 1097 8099 3807 4128 989 6453 7012 3118

a. Test at the 5% level whether the 4 day work week shortens the driving distance.State the result of this test in terms of the data. Consider the confidence boundassociated with this test. Does it influence the decision to go to the 4-day week?Why or why not?

b. Compute the power of this test with a difference of 500. Does it influence thedecision?

c. Do a 2-sided test at the 5% level to test whether there is a statistically significantdifference in the driving distances. What is the probability of Type II error withthis test? Does this test influence the decision to go to the 4-day week? Whatfactors other than the data presented might the manager want to consider?

I know you use the Paired T test in minitab. Please explain each step.