STAT212
EXAMPLES
1. Twenty volunteers at a cold research institute caught a cold after after having been exposed to various cold
viruses. Ten of the volunteers were randomly selected to receive tablets containing 1 gram of vitamin C. These
tablets were taken four times a day. The control group, consisting of the other 10 volunteers, was given placebo
tablets that looked and tasted exactly like the vitamin C ones. This was continued for each volunteer until a doctor,
who did not know whether one volunteer was receiving vitamin C or the placebo, decided that the volunteer was no
longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the experiment,
the following data resulted:
Treated With Vitamin C
5.5
6.0
7.0
6.0
7.5
7.5
5.5
7.0
6.5
6.0
Treated With Placebo
6.5
6.0
8.5
7.0
6.5
7.5
6.5
7.5
6.0
8.0
Is there sufficient evidence to conclude that the mean time for patients treated with vitamin C is less than the mean
time for the patients treated with placebo? Use =.05.
2. In the past, many bodily functions were thought to be beyond conscious control. However, recent experimentation
suggests that it may be possible for a person to control certain bodily functions if that person is trained in a program
of biofeedback exercises. An experiment is conducted to show that blood pressure levels can be consciously reduced
in people trained in this program. The blood pressure measurements (in millimeters of mercury) listed in the table
represent readings before and after the biofeedback training of six subjects. Is there sufficient evidence to conclude
that the mean blood pressure after people are trained in this program is less than the mean blood pressure before
training? Use =.05.
Subject
Before
After
1
136.9
130.2
2
201.4
180.7
3
166.8
149.6
4
150
153.2
5
173.2
162.6
6
169.3
160.1
3. An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep.
A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into
two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After a
6-month period, the lambs were slaughtered and the following worm counts were recorded.
Drug-Treated Sheep
Untreated Sheep
18
40
43
54
28
26
50
63
16
21
32
37
13
39
35
23
38
48
33
58
6
28
7
39
Test whether the mean number of tapeworms in the stomachs of treated lambs is less than the mean for untreated
lambs. Use =.05.
4. Children with Down Syndrome generally show a pattern of retarded mental development, although some achieve
higher intellectual levels than others. The intellectual achievements of Down Syndrome children have been studied
by numerous investigations, and several different types of chromosomal abnormalities associated with the syndrome
have been identified. Two such abnormalities are called trisomy 21 and mosaicism. The levels of intellectual
functioning of trisomy 21 and Mosaic Down Syndrome were compared in the paper “Mental Development in Down
Syndrome Mosaicism” (American Journal of Mental Retardation (1991): 345-351).
Thirty children with mosaic Down Syndrome who were treated at USC Medical Center were selected to participate
in the research project. The investigators then chose 30 children with trisomy 21 Down Syndrome from among 350
who had been seen at the medical center. The 30 chosen were selected (with the help of the computer) to achieve the
best possible matches for children in the mosaic group, using age, sex, and parental socioeconomic status as the
criteria for matching. The result was 30 matched pairs of children. IQ levels for all the children were determined.
The researchers proposed using the data to test the theory that children with mosaic Down Syndrome generally
achieve higher intellectual levels. Use =.05.
Pair
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Mosaic
73
43
69
89
53
81
59
71
65
53
58
55
61
63
87
64
63
58
50
59
75
61
71
92
57
76
Trisomy 21
71
53
58
71
50
70
55
18
31
57
63
60
48
55
59
78
55
51
55
53
47
50
47
44
28
75
27
28
29
30
91
43
55
88
63
46
54
48