Download Practice Exam 2

Practice Exam 1
Public Health 6415
1. The value of diet, exercise and meditation was studied in 16 hypertensive women. The
researchers believe these women will observe a change in their diastolic blood pressure
after 4 months in the experimental program. The pretrial mean diastolic blood pressure
of study participants is 120 mm Hg; their post-trial diastolic pressure is 115. Assume
normality of the relevant distributions. Is there a difference in the mean diastolic blood
pressure? Use  = 0.05 , assume the standard deviation of the sample difference of
before to after to be s=8.
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2. Two brands of cigarettes are selected, and their nicotine content is compared. The data
are shown here. Test the hypothesis that the means are different using =0.01. State
your null and alternative hypotheses, size of the test, test statistic and value, p-value and
conclusion. Assume all relevant distributions are approximately normal. (Hint: can you
assume 1=2?)
Brand A
Mean = 28.6 milligrams
s = 5.1 milligrams
n=35
Brand B
Mean = 32.9 milligrams
s=4.4 milligrams
n=27
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3. A researcher wishes to try three different techniques to lower the blood pressure of
individuals diagnosed with high blood pressure. The subjects are randomly assigned to
three groups; the first group takes medication, the second group exercises, and the third
group follows a special diet. After four weeks, the reduction in each person’s blood
pressure is recorded. At =0.05, test the claim that there is no difference among the
means. Use the SAS output below to help you test this hypothesis.
ANOVA for Blood Pressure Change
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11:00 Friday, February 10, 2006
The ANOVA Procedure
Class Level Information
Class
Levels
group
3
Values
d e m
Number of Observations Read
Number of Observations Used
15
15
Anova for Blood Pressure Change
2
11:00 Friday, February 10, 2006
The ANOVA Procedure
Dependent Variable: change
Source
DF
Sum of
Squares
Mean Square
F Value
Pr > F
Model
2
160.1333333
80.0666667
9.17
0.0038
Error
12
104.8000000
8.7333333
Corrected Total
14
264.9333333
R-Square
Coeff Var
Root MSE
change Mean
0.604429
38.21407
2.955221
7.733333
Source
DF
Anova SS
Mean Square
F Value
Pr > F
group
2
160.1333333
80.0666667
9.17
0.0038
Anova for Blood Pressure Change
11:00 Friday, February 10, 2006
The ANOVA Procedure
Level of
group
N
------------change----------Mean
Std Dev
3
d
e
m
5
5
5
7.6000000
3.8000000
11.8000000
3.20936131
3.19374388
2.38746728
Hypothesis test: State your null and alternative hypotheses, test statistic, pvalue and
conclusion.
More on question 3:
a. How many degrees of freedom are there for sum of squares between?
b. What is the value of the mean of squares between? What does it represent?
c. How many degrees of freedom are there for the sum of squares within?
d. What is the value of the mean of squares within? What does it represent?
e. Can we conclude there is a difference between the diet and exercise group?
4. Transient hypothyroxinemia, a common finding in premature infants, is not thought to
have long-term consequences, or to require treatment. A study was performed to
investigate whether hypothyroxinemia in premature infants is a cause of subsequent
motor and cognitive abnormalities. Blood thyroxine values were obtained on routine
screening in the first week of life from 536 infants who weighed 2000g or less at birth
and were born at 33 weeks gestation or earlier. The data that follows were presented
concerning the relationship between mean thyroxine level and gestational age.
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Gestational Age (x)
<24
25
26
27
28
29
30
31
32
33
Mean Thyroxide
Level ug/dL (y)
6.5
7.1
7.0
7.1
7.2
7.1
8.1
8.7
9.5
10.1
These data were analyzed using SAS. The output follows. Use this output to answer
questions.
The REG Procedure
Dependent Variable: thy
Number of Observations Read
Number of Observations Used
10
10
Analysis of Variance
5
DF
Sum of
Squares
Mean
Square
1
8
9
11.12836
2.09564
13.22400
11.12836
0.26195
Root MSE
Dependent Mean
Coeff Var
0.51181
7.84000
6.52825
Source
Model
Error
Corrected Total
R-Square
Adj R-Sq
F Value
Pr > F
42.48
0.0002
0.8415
0.8217
Parameter Estimates
Variable
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
Intercept
age
1
1
-2.62727
0.36727
1.61408
0.05635
-1.63
6.52
0.1422
0.0002
95% Confidence Limits
-6.34935
0.23733
1.09480
0.49721
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A.
Which is the dependent variable?
Which is the independent variable?
B.
What is the equation for the least squares regression line for this data?
C.
Does there appear to be a linear association between mean thyroxine level and gestational age?
Use the correlation to answer this question. If so, what is the strength and direction of this
association?
D.
Test the null hypothesis that the correlation is zero vs. it is not zero.
E.
How much of the variation in mean thyroxine level is explained by the regression line of mean
thyroxine level on gestational age?
F.
There were originally 536 infants in the study but we only have 10 observation points.
G.
Do you think the regression line for the original data or the 10 observations has a larger RSquare value?
H.
What is the expected mean value of thyroxine level for a baby whose gestational age is 27 weeks?
Why?
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I.
What is the expected mean value of thyroxine level for a baby whose gestational age is 40 weeks?
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