Appendix A
Additional Problems
The problems in this document may
be used as extra review or practice for quizzes and exams. They are
organized by chapter and are very similar in spirit to those found in the
text. When referring to problems in this document, we will use the chapter
number followed by the problem number. For example, Problem 1.3 refers to
the third problem in the problem set for Chapter 1. The answers to these
problems may be found in a companion document at this website.
Problems for Chapter 8
- To test
the effectiveness of four different sunblock formulations (treatments) ,
each formulation was applied to the backs of 3 randomly selected subjects
from a group of 12 volunteers. At the end of a 4-hour exposure to bright
sunlight, each subject was evaluated for sunburn damage and ranked, with
rank #1 indicating the least damage and rank #12 indicating the most
damage. The ranked data are summarized below. Carry out an appropriate
test to determine whether there were differences among the treatments, and
if so, locate the treatments that are different.
| Treatment |
I |
II |
III |
IV |
| ni |
3 |
3 |
3 |
3 |
| Mean rank Ri/ni |
5.33 |
10.83 |
2.33 |
7.5 |
- Current
fitness industry trends include a growing interest in non-competitive
boxing programs. A study was conducted to examine the physiological
responses of punching at various tempos. Using commercially available
boxing equipment, 48 male boxing-trained subjects performed straight left
and right punches at one of four different tempos (60, 80, 100, and 120
punches per minute) . Each trial lasted two minutes, similar to that of
traditional boxing round training. Oxygen consumption (ml/ kg/ min), and
heart rate (bpm) were monitored continuously during each round using open
circuit spirometry and telemetry. Summary data are recorded below. (Based
on concepts in L. Kravitz, et al. , Metabolic effect of punching tempo,
www.unm.edu/~lkravitz/Research%20Abstrs/punchingtempo.html.)
- Use ANOVA to determine whether there is a
difference in oxygen consumption among the various tempos. If so, which
pairs are different? (Use DMRT.)
| Punches/min |
60 |
80 |
100 |
120 |
Total |
| ni |
12 |
12 |
12 |
12 |
48 |
|
 i
|
25.2 |
28.0 |
28.3 |
29.9 |
|
| si |
3.2 |
3.4 |
3.0 |
3.1 |
|
| Ti |
302.4 |
336 |
339.6 |
358.8 |
1336.8 |
- Determine whether there is a difference in heart
rates among the various tempos. If so, which pairs are different?
| Bpm |
60 |
80 |
100 |
120 |
Total |
| ni |
12 |
12 |
12 |
12 |
48 |
| i |
164.7 |
173.3 |
176.3 |
182.1 |
|
| si |
13.1 |
11.9 |
11.1 |
9.9 |
|
| Ti |
1976.4 |
2079.6 |
2115.6 |
2185.2 |
8356.8 |
|
