Please, submit your homework right after lecture on the due date. See
the
HW
submission rules. On the front page include the
following
header.
- (HW_8)
- Do these problems on pages 316-386 from Samuels
& Witmer's text Statistics for the Life
Sciences, Prentice Hall (2003).
- 8.4: In a study of 1,040
subjects researchers found that the prevalence of coronary heart
disease increased as the number of cups of coffee consumed per day
increased:
- What is the
explanatory variable?
- What is the response
variable?
- What are the
observational units?
- 8.9: Olestra is a
no-calorie, no-fat additive that is used in the production of some
potato chips. After the US FDA approved the use of olestra some
consumers complained of Olestra induced stomach cramps and diarrhea. A
randomized double-blinded experiment was conducted in which some
participants were given bags of chips made with olestra and others were
given ordinary potato chips. In the olestra group, 38 % of the subjects
reported having gastrointestinal symptoms. In the group eating the
regular chips that number was 37%. (The two percentages are not
statistically significantly different). Explain how the placebo
effect/no-placebo effect is related in this experiment. Also, explain
why was it important to do this as a double-blinded study.
- 8.20: In a
pharmacological experiment on eating behavior in rats, 18 rats are to
be randomly allocated to 3 treatments (T1, T2 and T3). During the
experiment, the animals are kept in cages in a rack. The rack has 3
tears with 6 cages per tear. Lighting conditions varied somewhat
between different tiers (bottom rack is darkest). It's known that
lighting conditions correlate with eating behavior in rats. Rank (best
to worst) these three plans proposed for allocation of the rats to
cages. Explain your choices.
- Plan I: Randomly
allocate the 18 rats to the 18 cages
- Plan II: Put the
T1 rats in tier 1, T2 rats in tier 2 and T3 rats in T3.
- Plan III: On each tier
put 2 rats from each of the 3 treatments.
- 8.29: SUppose someone
conducts a randomized response sample, as explained in example 8.28,
and find that 43 out of 104 people answered "Yes". What is the
resulting estimate of p. the population percentage for whom the
truthful answer to the sensitive question is "Yes"?
- 9.19: Twenty institutionalized epileptic patients
participated in a study of a new anticonvulsant drug, Valproate. Ten of
the patients (chosen at random)
were started on the daily Valproate and the other ten received an
identical placebo pill. During an eight-week observation period, the
number of major and minor seizures were counted. After this, the
patients were “crossed over” to the other treatment, and seizure counts
were made during a second eight week observation period. We would use
the independent / dependent (paired) samples method in order to conduct
a test of hypothesis. (Note that this analysis ignores the possible
effect of time, that is, first vs. second observation period).
Patient
Number
|
Placebo
Period
|
Valproate
Period
|
1
|
37
|
5
|
2
|
52
|
22
|
3
|
63
|
41
|
4
|
2
|
4
|
5
|
25
|
32
|
6
|
29
|
20
|
7
|
15
|
10
|
8
|
52
|
25
|
9
|
19
|
17
|
10
|
12
|
14
|
11
|
7
|
8
|
12
|
9
|
8
|
13
|
65
|
30
|
14
|
52
|
22
|
15
|
6
|
11
|
16
|
17
|
1
|
17
|
54
|
31
|
18
|
27
|
15
|
19
|
36
|
13
|
20
|
5
|
5
|
- 9.33: In an investigation of possible brain damage due to
alcoholism, an X-ray procedure known as a computerized tomography (CT)
scan was used to measure brain densities in eleven chronic alcoholics.
For each alcoholic, a nonalcoholic control was selected who matched the
alcoholic on age, sex, education, and other factors. The brain density
measurements on the alcoholics and the matched controls are reported in
the accompanying table. Use an appropriate statistical test (justify
your choice) to assess a null hypothesis of no difference against the
alternative that alcoholism reduces brain density at a=0.02.
| Pair |
Alcoholic |
Control |
Difference |
| 1 |
40.1 |
41.3 |
-1.2 |
| 2 |
38.5 |
40.2 |
-1.7 |
| 3 |
36.9 |
37.4 |
-0.5 |
| 4 |
41.4 |
46.1 |
-4.7 |
| 5 |
40.6 |
43.9 |
-3.3 |
| 6 |
42.3 |
41.9 |
.4 |
| 7 |
37.2 |
39.9 |
-2.7 |
| 8 |
38.6 |
40.4 |
-1.8
|
| 9 |
38.5 |
38.6 |
-0.1 |
| 10 |
38.4 |
38.1 |
.3 |
| 11 |
38.1 |
39.5 |
-1.4 |
| Mean |
39.14 |
40.66 |
-1.52
|
| SD |
1.72 |
2.56 |
1.58 |
- Practice problems (Do not
turn in): 10.4, 10.5, 10.6, 10.11,
10.17, 10.22, 10.35, 10.37, 10.73, 10.87, 10.96 - pages 400-461,
Samuels & Witmer's text Statistics for the Life Sciences,
Prentice Hall (2003).
