FINAL EXAM
CIVL 7012
Due no later than 5:30 p.m. 05/06/09
Since this is a take-home exam, you are to neither solicit nor receive any form of
help other than that specified below. You are to have no conversation with your
classmates regarding the exam. I am willing to answer questions concerning any
misunderstandings you may have regarding the problems themselves. You may use
your text, handout material from this course, or notes. The use of homework,
quizzes, or final exams from previous semesters of this course is PROHIBITED!
1. An experiment was performed to determine whether the annealing temperature of
ductile iron affects its tensile strength. Five specimens were annealed at each of
four temperatures. The tensile strength (in ksi) was measured for each. The
results are presented in the following table.
a. Construct an ANOVA table. You must show all calculations for this
problem (i.e. do not use the ANOVA Toolpack in Excel).
b. Can you conclude that the tensile strength varies with temperature?
c. Plot average tensile strength against temperature and interpret the results.
d. Use Fisher’s LSD method with alpha = 0.05 to analyze the means of
tensile strength at the four different temperatures.
Temperature
(ºC)
750
800
850
900
2.
19.72
16.01
16.66
16.93
Tensile Strength
(ksi)
20.88 19.63 18.68
20.04 18.10 20.28
17.38 14.49 18.21
14.49 16.15 15.53
17.89
20.53
15.58
13.25
A foundation engineer estimates that the settlement of a proposed structure will
not exceed 2 in. with 95% probability. From a record of performance of many
similar structures built on similar soil conditions, he finds that the coefficient of
variation of settlement is about 20%. If a normal distribution is assumed for the
settlement of the proposed structure, what is the probability that the proposed
structure will settle more than 2.5 inches?
3. The following is the 10-yr record of floods between 1994 and 2003 in a particular
town. The occurrences of floods in the town may be modeled as a Poisson
process.
a. On the basis of the above historical flood data, determine the probability
that there will be between one and three floods in the town over the next 3
years.
b. A sewage treatment plant is located on a high ground in the town. The
probability that it will be inundated during a flood is 0.02. What is the
probability that the treatment plant will not be inundated for a period of 5
years?
Year
1994
1995
1996
1997
1998
Number of Floods
1
0
1
1
0
Year
1999
2000
2001
2002
2003
Number of Floods
0
2
0
0
1
4. A self-standing antenna disk is supported by a lattice structure that is anchored to
the ground at the base. During a wind storm, the disk may be damaged as a result
of anchorage failure and/or failure of the lattice structure. Suppose the following
information is known:
I. The probability of anchorage failure during a wind storm is 0.006
II. If the anchorage should fail, the probability of failure of the lattice structures
will be 0.40, whereas the probability of failure of the anchorage given that
failure has occurred in the lattice structure is 0.30.
Determine the following:
a. The probability of damage to the antenna disk during a wind storm.
b. The probability that only one of the two potential failure modes will occur
during a wind storm.
c. If the disk is damaged during a wind storm, what is the probability that it
was caused only by anchorage failure?
5. The data in the table below are radium-226 levels (measured in pCi/L) for 12 soil
specimens collected in southern Dade County, Fl. Utilize the nonparametric sign
test to determine whether the median radium-226 level in the soil in southern
Dade County exceeds the Environmental Protection Agency limit of 4.0 pCi/L,
using α= 0.10.
1.46
1.30
5.92
0.58
8.24
1.86
4.31
3.51
1.41
1.02
6.87
1.70
6. The following are data on the breaking strength (in pounds) of 2 kinds of material.
Use the Wilcoxon Rank-Sum test at the 0.05 level of significance to test the claim
that the strength of Material 1 is stochastically larger than the strength of Material
2.
Material 1
Material 2
144
175
181
164
200
172
187
194
169
176
171
198
186
154
194
134
7. The article “Multiple Linear Regression for Lake Ice and Lake Temperature
Characteristics” (S. Gao and H. Stefan, Journal of Cold Regions Engineering,
1999:59-57) presents data on maximum ice thickness in mm (y), average number
of days per year of ice cover(x1), average number of days the bottom temperature
is lower than 8 degrees C (x2), and the average snow depth in mm (x3) for 13
lakes in Minnesota. The data are presented in the following table.
a. Fit a multiple regression model to the data below (using all three x
variables).
b. Test for significance of regression.
c. Test the hypothesis that β3 = 0.
d. Construct a 95% confidence interval for β2.
e. Build an appropriate regression model using backward elimination.
f. If two lakes differ by 2 in the average number of days per year of ice
cover, with other variables being equal, by how much would you expect
their maximum ice thicknesses to differ?
Y
730
760
850
840
720
730
840
730
650
850
740
820
710
x1
152
173
166
161
152
153
166
157
136
142
151
145
147
x2
198
201
202
202
198
205
204
204
172
218
207
209
190
x3
91
81
69
72
91
91
70
90
47
59
88
60
63
8. The ratio of observed to calculated settlements for piles is a measure of the
accuracy of the method used to calculate the settlement. Given the data in the
table below:
a. Perform a chi-square goodness-of-fit test for the normal distribution at the
5% significance level.
b. Perform a K-S test for the same value of alpha.
c. What can you conclude from these tests?
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Ration of Observed to Calculated
Settlement
0.12
2.37
1.02
0.94
1
0.97
0.88
1.04
1.06
0.86
0.86
0.92
0.99
1.38
0.82
1.14
1.01
0.87
1.04
0.84
0.94
0.99
0.52
1.18
1.09