Data were collected during a step-direction experiment in the biomechanics laboratory at Hope College. The goal of the study is to establish differences in stepping responses between healthy young and healthy older adults. In one part of the experiment, the subjects are told in what direction they should take a step. Then, when given a signal, the subject takes a step in that direction, and the time it takes for them to lift their foot to take the step is measured. The direction is repeated a few times throughout the testing, and for each subject, a mean of all the €œliftoff€ times in a certain direction is calculated.
The mean liftoff times (in thousandths of a second) for the anterior direction, ordered for your convenience, are as follows:

(a) Construct a back-to-back stem-and-leaf display. Use stems 3€¢, 4ˆ—, . . . , 9ˆ—.
(b) Use the Wilcoxon statistic to test the null hypothesis that the response times are equal against the alternative that the times for the young subjects are less than that for the older subjects.
(c) What outcome does a t test give?

Young Subjects 397 433 450 468 485 488 498 504 561 565 569 576 577 579 581 586 696 Older Subjects 463 538 549 573 588 590 594 626 627 653 674 728 818 835 863 888 936