16.37 Marketing a health aid.
Exercise that helps health and fitness should raise our heart rate for some period of time. A firm that markets a “Step Up to Health” apparatus consisting of a step and handrails for users to hold must tell buyers how to use their new device. The firm has subjects use the step at several stepping rates and measures their heart rates before and after stepping. Here are data for five subjects and two treatments: low rate (14 steps per minute) and medium rate (21 steps per minute). For each subject, we give the resting heart rate (beats per minutes) and the heart rate at the end of the exercise.12
heart
16-23
| Low rate | Medium rate | |||
| Subject | Resting | Final | Resting | Final |
| 1 | 60 | 75 | 63 | 84 |
| 2 | 90 | 99 | 69 | 93 |
| 3 | 87 | 93 | 81 | 96 |
| 4 | 78 | 87 | 75 | 90 |
| 5 | 84 | 84 | 90 | 108 |
Does exercise at the low rate raise heart rate significantly? State hypotheses in terms of the median increase in heart rate and apply the Wilcoxon signed rank test. What do you conclude?
16.37
H0: median , Ha: median . . , . , . The data do not show a systematic difference in heart rate.