You have simulated two alterative designs for the shuttle bus operation in the campus using independent random numbers in 4 replications. You have obtained the average service times (in minutes) for the two designs as follows: Replication 1 2 3 Average service time (min) Design Design 2 13 22 11 24 10 23 14 20 12.00 22.25 1.83 1.71 Average Standard Deviation a) Assuming that the difference between the variances of the two designs is negligible can you say that one design is statistically better than the other at a 95% confidence level? Which one? (20 points) b) The students who use the shuttle bus indicated that less than a 5 minute improvement in the service time is insignificant to them. Taking this into account, can you say that one design is better than the other? Explain why. (7 points) c) Suppose that you have also simulated the current shuttle bus operation and compared the current system with Design I and Design 2 at a 95% confidence level. What is the overall confidence level of the three comparisons you have made? (6 points)