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 1
- Medical researchers are
testing a new chemotherapy regime for colon cancer. A group of 100 male
patients volunteer for the program. Of these, 50 are selected at random to
receive the new therapy regime (experimental group) while the remaining 50
will receive the current standard regime (control group). The ages of the
subjects are given below.
| 20 41 48 53 59 28 43 49 54 61 |
| 23 42 48 53
59 30 43 49 54 62 |
| 24 42 48 53
60 32 44 49 55 62 |
| 25 42 48 53
60 33 44 50 55 63 |
| 27 43 49 54
61 35 44 50 55 64 |
| 36 45 50 56
65 39 46 51 56 73 |
| 37 45 50 56
67 40 47 52 57 75 |
| 38 45 51 56
68 40 47 52 58 76 |
| 38 46 51 57
70 41 47 52 59 78 |
| 39 46 51 57
72 41 47 52 59 80
|
Do both data sets
satisfy the 30-300 rule?
Produce a five-number
summary and a corresponding box plot for each group of data.
The researchers assumed
that there were no significant differences in the ages of the subjects
in the two groups. Do you agree? Justify your answer.
The Southern cavefish, Typhlichthys subterranus, is found mostly in the
dolomite aquifiers of the Salem Plateau in the South Central Ozarks. A
population of 17 individuals was recently discovered in a small cave in
central Missouri. The length of each individual was measured (in cm) and
is recorded below.
| 3.8
6.6 3.2 3.9 4.5 6.8 |
| 4.0 2.8
3.0 3.5 3.8 3.9 |
| 4.3 4.6
6.0 4.9 2.9 |
Find the population mean, the
uncorrected sum of squares, the correction term, the corrected sum of
squares, the population variance, and the population standard deviation.
Absolute pitch is thought by some to consist of two components: a relative common
ability, pitch memory, and a more rare ability, pitch labeling. To investigate pitch memory, 46 undergraduates were asked to select one of 58 CDs which contained
popular songs ( e.g., "Hotel California" by the Eagles and "Every Breath You Take" by the Police). Without listening to the song they selected, they were asked to reproduce
( sing, whistle, hum) the tones of the song that they claimed to know very
well. The subjects were recorded on digital audio tape and their reproductions
were compared to the actual tones of the artists on the CD. Errors were measured
in semitone deviations from the correct pitch. As is standard in such work,
octave errors were not penalized ( on the assumption that subjects with pitch
memory may have a stronger representation for pitch class than pitch height). That is,
an octave was added or subtracted, as necessary, to the tones produced until all
tones fell within one-half octave (six semitones) on either side of the target
tone. A summary of the data is given below. (Based on data from Daniel J.
Levitin, 1994, "Absolute memory for musical pitch: Evidence from the production
of learned melodies," Perception & Pyschophysics, 56 (4): 414423.)
| Error
(semitones)
|
Frequency |
| -6 |
1 |
| -5 |
3 |
| -4 |
4 |
| -3 |
4 |
| -2 |
4 |
| -1 |
8 |
| 0 |
12 |
| 1 |
6 |
| 2 |
1 |
| 3 |
1 |
| 4 |
1 |
| 5 |
1 |
| 6 |
0 |
| Total |
46 |
- Make a table of relative frequencies, cumulative
frequencies, and relative cumulative frequencies for these data.
- Make a relative frequency histogram of these data.
- Compute the mean, variance, and standard deviation
for these data.
- Do
these data exhibit the so-called "lounge singer effect" widely noted by
vocal instructors, wherein amateur singers tend to undershoot tones and
to sing flat? Justify your answer.
