A plant manager, in deciding whether to purchase a machine of design A or design B, checks the times for completing a certain task on each machine. Eight technicians were used in the experiment, with each technician using both machine A and machine B in a randomized order. The times (in seconds) required to complete the task are given in the accompanying table.
| Techician |
A |
B |
| 1 |
32 |
30 |
| 2 |
40 |
39 |
| 3 |
42 |
42 |
| 4 |
26 |
23 |
| 5 |
35 |
36 |
| 6 |
29 |
27 |
| 7 |
45 |
41 |
| 8 |
22 |
21 |
a Test to see if there is a significant difference between mean completion times, at the 5% significance level.
b Do you think pairing on technicians was worthwhile in this case? Explain.
c What assumptions are necessary for the test in part (a)?