1. A company is contemplating redesigning one of its business process to reduce the time required to complete the process and reduce operating costs. The company has developed a simulation model for its current process design and two proposed design changes. 20 replications were performed using common random numbers. The following table displays the completion times in hours for the current design and each proposed design.

Replication	Completion Time Current Design (hours)	Completion Time Proposed Design A (hours)	Completion Time Proposed Design B (hours)
1	8.11	7.52	6.81
2	11.78	13.35	8.90
3	10.43	11.55	8.00
4	7.71	6.66	7.17
5	10.80	11.43	7.52
6	7.68	7.43	6.70
7	11.36	11.09	8.38
8	10.11	10.26	7.73
9	11.10	13.60	8.87
10	8.20	11.87	8.33
11	8.92	9.27	7.49
12	12.96	14.73	9.87
13	11.47	14.01	8.87
14	8.48	7.33	7.44
15	11.88	12.57	9.47
16	8.45	8.18	7.37
17	12.50	12.20	9.22
18	11.13	11.29	8.51
19	12.67	16.21	10.48
20	8.18	14.16	9.16

1. Plot the replication completion times for each design and discuss the extent to which the completion times appear to be correlated, including discussing whether the observed correlation is positive or negative. (10 points)
2. Calculate the sample mean and variance for the completion times for each design and discuss the apparent effectiveness of the proposed design changes with respect to reducing the process completion time. (10 points)
3. Calculate a 95% confidence interval for the difference between the following: (15 points)
   1. Current design and proposed design A
   2. Current design and proposed design B
   3. Proposed design A and proposed design B
4. Discuss the implications of the confidence intervals with respect to the effect of the proposed design changes on the process completion time. (15 points)