STA 6167 – Exam 2 Spring 2009
PRINT Name ________________
Part 1. A study was conducted to measure the effects of age and motorcycle riding on the
incidence of erectile dysfunction (ED). Men were classified by age (20-29,30-39,4049,and 50-59), where the midpoints (25,35,45, and 55) were used as the age levels, and
mtrcycl was classified as 1 if motorcycle rider and 0 if not. The variable mtcrage was
obtained by taking the product of age and mtrcycl. The following models were fit (where
 is the probability the man suffers from ED:
Model 0 :  
e
1  e
- 2ln(L 0 )  1349.16
e   A A  M M   AM AM
Model1 :  (Age, MR) 
1  e   A A  M M   AM AM
 2 ln( L1 )  1250.34
Model 0:
Model 1:
Test H0: A = M = AM = 0 at the  = 0.05 significance level:
Test Statistic:
Rejection Region:
Does the “effect” of age differ among motorcycle riders and non-motorcycle riders?
H0: ______
HA: _____ TS: _________ P-value ______ Yes / No
Give the predicted values for Models 0 and 1 for age=25/mtrcycl=0 and 55/1
Model 0: 25/0 __________________
55/1 _______________________
Model 1: 25/0 __________________
55/1 _______________________
Part 2: A substance is used in biomedical research and shipped by airfreight in cartons of
1000 ampules. Data from n=10 were collected where X = the number of aircraft transfers
(0,1,2,3) and Y = the number of broken ampules. A Poisson regression model was fit
where the (natural) log of the expected number of broken ampules is linearly related to
the number of transfers:
ln() = X
 0  2.341 SE   0   0.1338  1  0.215 SE   1   0.0828
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^
^
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Test whether there is a positive association between the number of broken ampules and
the number of transfers using the Wald “z-test” with =0.05.
H0: 1 = 0
HA: 1 > 0
Test Stat: ________________________
Rejection Region: __________________
Give the estimated means for X=0,1,2 transfers:
Part 3: A model is fit by a mining engineer to relate the angles of subsidence of
excavation sights (Y) to the ratio of the width to the depth of the mine (X, ranging from
0.34 to 2.17). She fits the following model based on Mitcherlich’s Law of Diminishing
marginal Returns based on n=16 wells:
yi   0 1  exp  1 xi    i
 0  32.46 SE   0   2.65  1  1.51 SE   1   0.30
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^
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The first well had x1=1.11 and y1=33.6. Give its predicted value and residual:
Predicted: ___________________ Residual ________________________
Compute a 95% Confidence Interval for the maximum mean angle (Hint, use the tdistribution for the critical value):
Part 4: An Analysis of Covariance is conducted to compare three exercise regimens with respect
to conditioning. Each participant is given a test to measure their baseline strength prior to training
(X). Out of the 30 participants, 10 are assigned to method 1 (Z1=1, Z2=0), 10 are assigned to
method 2 (Z1=0, Z2=1), and the remaining 10 receive method 3 (Z1=0, Z2=0). After training, each
participant is given a test of their strength (Y) .
Model 1: E(Y) =  +  X
Model 2: E(Y) =  +  X + 1Z1 + 2Z2
Model 3: E(Y) =  +  X + 1Z1 + 2Z2+ 1XZ1 + 2XZ2



R12 = 0.204
R22 = 0.438
R32 = 0.534
a) Test whether the slopes relating Y to X differ for the three exercise regimen.
i.
Null /Alternative Hypotheses:
ii.
Test Statistic:
iii.
Rejection Region/Conclusion:
b) Based on Model 2, test whether the three regimens differ, after controlling for X
i.
Null / Alternative Hypotheses:
ii.
Test Statistic:
iii.
Rejection Region/Conclusion:
c) Give the adjusted means for the 3 regimens for Model 2. (X-bar=29)
Coefficientsa
Model
1
2
3
(Constant)
X
(Constant)
X
Z1
Z2
(Constant)
X
Z1
Z2
XZ1
XZ2
Unstandardized
Coefficients
B
Std. Error
18.088
7.382
.676
.252
17.258
7.639
.721
.238
3.224
2.590
-4.650
2.503
9.456
11.772
.970
.373
28.333
15.588
-12.390
17.222
-.885
.526
.299
.577
a. Dependent Variable: Y
Standardized
Coefficients
Beta
.452
.482
.228
-.328
.649
2.002
-.875
-1.735
.606
t
2.450
2.683
2.259
3.030
1.245
-1.857
.803
2.604
1.818
-.719
-1.684
.519
Sig.
.021
.012
.032
.005
.224
.075
.430
.016
.082
.479
.105
.609
Match the Plot to the Exam Part. When there are more than one model and
group, identify which model is plotted and identify the groups.
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0
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0