Chapter 15.3, Problem 8E

Refer to Exercise 12.15. Using the sign test, do you find sufficient evidence to support concluding that completion times differ for the two populations? Use α = .10.

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.

1. a Test to see if there is a significant difference between mean completion times, at the 5% significance level.
2. b Do you think pairing on technicians was worthwhile in this case? Explain.
3. c What assumptions are necessary for the test in part (a)?