DPHS 568 Biostatistics in Dentistry, Summer 2006
Homework #1
Due July 19, 2006 (beginning of class). If more than one sheet, please staple.
Table 1
i
xi
1
4
2
-3
4
1. Using the data in Table 1 evaluate
 xi , and
i 1
3
8
4
2
4
x
i 1
2
i
.
2. Refer to the data in Table 2: Mercury Vapor Data.
a. Compute the mean, median and standard deviation of the urinary-Hg
values for all the study participants.
b. Draw a histogram describing urinary-Hg data.
3. Refer to the data in Table 2: Mercury Vapor Data.
a. Compute appropriate descriptive statistics comparing the case and control
participants with respect to fish consumption.
b. Present this comparison using boxplots.
c. What is your overall impression concerning the fish consumption in the
two groups?
4. In the NHANES3 dataset the percentage of 25-34 year-olds with a decayed,
missing or filled (DMF) upper left first bicuspid is about 35%. Similarly 35% of
these people have a DMF upper right first bicuspid. Both upper first bicuspids are
DMF in 28% of this cohort.
a. Do these data imply that DMF in the upper left first bicuspid is
independent of DMF in the upper right first bicuspid?
b. What is the probability that someone has at least one DMF upper first
bicuspid?
c. What is the conditional probability that the upper left first bicuspid is
DMF if the upper right one is?
d. What is the conditional probability that the upper left first bicuspid is
DMF if the upper right one is not? (Hint: Venn diagram may help.)
5. Suppose we planned to use periodontal assessment as a diagnostic test for future
CHD risk. We can evaluate the worth of this diagnostic marker using the data in
Table 3: Periodontal disease vs. future CHD risk. Consider the “disease” in this
case to be developing CHD within 10 years.
a. Compute the sensitivity and specificity of the test if we label someone as
positive if they have periodontitis or are edentulous.
b. Compute the relative risk of developing CHD within 10 years if one either
has periodontitis or is edentulous as compared to someone with healthy
gums or gingivitis.
c. What different kinds of information are given by the answers to a. and b.?
6. Suppose 7 out of 18 students in a grade-school class develop influenza, whereas
the nationwide rate for grade-schoolers is 20%.
a. Is there evidence of an excessive number of cases in this class? That is,
compute the probability of having at least 7 cases in this class if the
nationwide rate holds true.
b. If the nationwide rate held true, how many kids would be expected to
develop influenza?
7. For individuals over 60 years of age in the NHANES 3 study, of those who had
never smoked 7% had periodontitis (as evidenced by at least one site out of 28
with attachment loss 6mm or greater) while 15% of former and current smokers
had periodontitis.
a. What is the probability that exactly 2 of 10 smokers has periodontitis?
b. What is the probability that at least 2 of 10 smokers have periodontitis?
c. Suppose we have a group of 10 smokers and 10 never smokers. Compute
the probability that exactly 3 have periodontitis. Hint: Using Excel could
help compute binomial probabilities.
8. Let Z be a Standard Normal random variable.
a. What is Pr(Z < 0.72)?
b. What is Pr(Z > 1.2)?
c. What is Pr(0.72 < Z < 1.20)?
9. Suppose that total carbohydrate intake in 12- to 14-year-old boys is normally
distributed with mean 124 g/1000 cal and standard deviation of 20 g/1000 cal.
a. What percentage of boys in this age range have carbohydrate intake above
140 g/1000 cal?
b. What percentage of boys in this age range have carbohydrate intake below
100 g/1000 cal?
c. Suppose we randomly sampled four such boys. What is the probability
that the average carbohydrate intake of these four boys would be above
140 g/1000 cal?
Table 2: Mercury Vapor Data
ID
GROUP*
age
daily inhaled Urinary Hg
occlusal total
amalgam amalgam Hg vapor (g (nmol Hg/l
surfaces surfaces Hg/24 hr)
creatinine)
Fish
consumption
(meals/month)
1
CASE
44
13
43
1.6
0.8
8.0
2
CASE
42
13
46
2.1
1.0
2.0
3
CASE
43
10
30
2.6
2.2
4.0
4
CASE
43
19
68
4.1
3.6
10.0
5
CASE
40
20
48
4.6
1.4
6.0
6
CASE
36
11
24
0.3
1.7
4.0
7
CASE
49
13
39
1.4
1.7
4.0
8
CASE
62
4
34
0.6
2.0
7.0
9
CASE
47
14
62
1.7
0.9
5.0
10
CASE
40
13
50
1.2
1.0
4.0
11
CONTROL
45
16
63
6.1
7.1
3.0
12
CONTROL
43
11
43
3.0
2.4
3.0
13
CONTROL
47
12
31
2.4
3.3
4.0
14
CONTROL
34
11
25
0.7
1.5
8.0
15
CONTROL
41
10
24
0.4
1.4
5.0
16
CONTROL
40
15
46
0.6
4.7
1.0
17
CONTROL
42
12
45
2.5
3.8
3.0
18
CONTROL
48
16
50
3.8
3.3
2.0
Data from: Berglund A, Molin M: "Mercury vapor release from dental amalgam in patients with
symptoms allegedly caused by amalgam fillings." European Journal of Oral Sciences
(1996): 104: 56-63
* "Cases" are participants complaining of symptoms possibly associated with mercury.
Table 3: NHANES I, : Periodontal disease vs. future CHD risk
10 year CHD
incidence
no
yes
Healthy
Gingivitis
Periodontal
classifcation
Perio.
Edentulous
Total
Total
Count
3622
187
3809
%
95.1
4.9
100
Count
2308
150
2458
%
93.9
6.1
100
Count
1657
258
1915
%
86.5
13.5
100
Count
1823
457
2280
%
80.0
20.0
100
Count
%
9410
89.9
1052
10.1
10462
100