Download SELECTED EXERCISES AS A SAMPLE of THE FINAL EXAM a

SELECTED EXERCISES AS A SAMPLE of THE FINAL EXAM
1. a. Find out if any is an outlier in the given data set and carry out your further
calculations accordingly reconstructing the stem and leaf graphs for each group of
patients.
b. Construct the frequency distribution tables from the stem and leaf garphs you’ve
reconstructed.
c. Using the frequency distribution tables you’ve constructed, calculate the mean and
the standard deviation for each group.
d. Test the null hypothesis 𝐻0: 𝜇1 = 𝜇2
against to the alternative hypothesis
𝐻1 : 𝜇1 < 𝜇2 at 1% significance level.
The length of time required to splint an avulsed tooth with alveolar fracture for
two groups of patients.
Group 1: 18 years old or younger
Group 2: Older than 18 years
Frequency
Stem
Leaf
Frequency
2
14
4
1 79
2 00111223344689
3 0234
1
2
13
1
4 2
2
Stem
Leaf
1 8
2 29
3 034555567788
9
4 23
2. Twelve patient charts were randomly pulled from the patient database. Diastolic blood
pressure (DBP) and systolic blood pressure (SBP) measurements of these 12 patients
were recorded to study the relationship between the two variables.
a.
b.
c.
d.
i
1
2
3
4
5
6
7
8
9
10
11
12
Evaluate the strength of the linear association between DBP and SBP.
Estimate DBP of a patient whose SBP is 160.
Which one is the response variable in the regression model?
Find the value of coefficient of determination and state what it indicates.
𝑥𝑖
𝑦𝑖
116
130
134
158
138
98
130
170
120
104
125
136
72
90
85
112
85
60
80
115
80
75
78
80
3. A dental researcher has collected the following data to compare the strength of two
types of bonding materials, Brand A and Brand B. In which brand the variability of
strength is smaller?
Brand A
43.5
(kg)
60.5
58.5
55.7
42.7
46.7
48.4
4.
Brand B
57.6
(kg)
39.8
40.8
47.8
66.4
55.2
Chewing tobacco has high levels of sugars and the users typically keep it in
their mouth a few hours at a time. Therefore, it may be cariogenic. A sample of 6
chewing tobacco users and 8 non-users, all of whom are non-smokers, are compared
with respect to the number of decayed or filled teeth(DFT). Two samples are involved
in this example; one sample of 6 subjects from a population of chewing tobacco users
and another sample of 8 from a population of non-users. The random variables of
interest are X and Y. X is the random variable representing the number of DFT for the
chewing tobacco users, and Y is the random variable representing the number of DFT
for the non-users. Suppose that a mistake had been committed by recording 28 DFT
instead of 15 for the third subject in the chewing tobacco group. Find the error this
would cause in computing the mean DFT.
Number of DFT.
Chew
Non-users
16 (X)
4
Tobacco
(Y)
19
6
15
3
20
6
12
1
17
6
5
7
5. The patients with
progressive loss of
steadilyworsening
Hyperpigmentation
Addison’s
cortisol and
fatigue, a
of the skin
disease (hypoadrenocorticism) experience slowly
aldosterone secretion, usually producing a chronic,
loss of appetite, and some weight loss.
or gingiva occurs often enough to raise a strong
suspicion of the disease, prompting further evaluation. Suppose there is a 1 in 100
chance that the patient has Addison’s disease when he has hyperpigmentation of the
gingivae, and a 5 in 10, 000 chance when he does not have hyperpigmentation of the
gingivae. What are the predictive value positive and the predictive value negative?
6. Dental patients are classified according to their age: young, middle-aged, and elderly.
They also are classified according to their tooth mobility: no mobility, class I, class II,
and class III.
a. What is the sample space  when you classify the patients according to their
age and tooth mobility?
b. If the elementary events are equilly likely what is the probability of randomly
selecting a young patient from this population?
c. Suppose the actual distribution of patients according to their age and mobility
is as follows, what is the probability of randomly selecting a young patient
being in the class III?
The distribution of patients according to their age and mobility
Mobility
Age
No mobility Class I Class II
Class III
Total
Young
0.15
0.04
0.05
0.07
0.31
Middle-aged
0.04
0.10
0.10
0.04
0.28
Elderly
0.01
0.11
0.20
0.09
0.41
Total
0.20
0.25
0.35
0.20
1.00
d. Let the event A and B be a patient is young and from class II, respectively.
State whether the events A and B are independent and/or mutually exclusive.
7. As of early January of 2012 there were 128 known cases of squamous cell carcinoma
patients who resided in Çubuk. Between January and June, 43 new cases were
reported in Çubuk where as of January, there were 10 250 people. However, in June
there were only 7, 750 residents, because most of the college students left town for the
summer. What is the prevalence rate as of January, and what is the incidence rate of
squamous cell carcinoma during the period between January and June for Çubuk?
8. Lung cancer is the number one cause of cancer deaths in both men and women in the
Turkey. Approximately 90, 100 Turks died from lung cancer in 2012. The
overwhelming majority of lung cancer, at least 90%, are caused by cigarette smoking
It was estimated that 75, 100 lung cancer deaths per year are caused by smoking. As of
2012 there are about 42.5 million adult Turks, of which 27.2 million are smokers.
What is the Relative Risk of deaths caused by cancer in Turkey ?
9. The primary factors shown to predispose to implant failure are low bone density (i.e.,
type IV bone) and smoking. In a prospective study of the early outcomes of 223
implants placed in 78 patients. The patients are divided into two groups: smokers and
non-smokers. The failure rate of the implants was observed. An implant removal for
any reason or an implant exhibiting more than 50% bone loss was considered a failure.
The research data are summarized in the following table. Find the ratio of odds in
favor of an implant failure for smokers to that of an implant failure for non-smokers.
Risk Factor
Smokers
Non-smokers
Total
Results of Implants
Failure
Success
9
38
10
166
19
204
Total No. of Implants
47
176
223
10. Let A be the event that a canine tooth is carious and B be the event that a canine tooth
is fractured. Let P(A) = 0.25 and P(B) = 0.20. If the probability that a canine tooth is
carious, given that it is fractured, is 0.45, what is the chance that a canine tooth is
fractured and carious?
11. An orthodontics researcher is interested in modeling the distribution of maxillary
teeth. He needs to measure the distance from mesial to mesial between two maxillary
second bicuspids. This requires all his subjects to have both second bicuspids. Let A
be the event that a patient has at least one missing second bicuspid. The age of the
subjects is divided into five classes as follows. What is the chance that a patient is 66
or older, given that she has at least one missing second bicuspid?
Age
Population(%)
With a Missing
Second Bicuspid (%)
Less than 20
21–35
36–50
51–65
66 or older
20
15
25
30
10
5
10
18
23
45
12. The producer of İpana was about to introduce a new mouthrinse product for the
prevention of gingivitis. The product was tentatively named Oral-Fresh. To study the
effectiveness of the product the investigators recruited 180 patients who met the
inclusion criteria. These subjects were randomly assigned to each of the three
treatment groups: Oral-Fresh, placebo, and peridex. Each treatment group contained
70 subjects. Specific instructions were given to the subjects regarding the use of the
treatments, such as the amount of mouthrinse and the rinsing time, to control the
experiment. The subject’s compliance with the products was carefully monitored. To
assess the effectiveness of the mouthrinse, the gingival index of each patient was
measured at the baseline and at the 3-month time point.
a. Which group is negative control group?
b. Which groups are positive control group?
c. If the paralel groups design is used in this research, how many measurements
are needed?
d. If the crossover groups design with three treatments is used in this research,
how many measurements are needed?