Statistics

CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
1 of 7
Name:__________________________________
Statistical Inference from Observational Data
Do your work on this template and scan into Gradescope!
1. You are renovating a historic steel moment frame building. Before proceeding on the
design, you have ordered that 10 steel coupons be taken from the existing beams and
columns of the structure and tested for yield strength. The following are the results of
the testing.
Sample Yield Stress (ksi)
1 38.83
2 37.17
3 35.59
4 38.21
5 34.01
6 34.79
7 37.87
8 37.66
9 36.13
10 33.80
a. (6 pts) Estimate the mean and standard deviation of the steel used in the
building.
Sample mean: ________________ ksi
Sample deviation: ________________ ksi
Sinar Alsosaymeh
mean 36,401 36.406
deviation S
XIII 29.31521
52 3.25725
36.41 5 1 805
1 81
CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
2 of 7
b. (6 pts) You suspect that the steel used was 36 ksi steel. To a 5% significance
level, do the tests support the null hypothesis that this is 36 ksi steel?
Z: ________________
Critical values: ________________
Null hypothesis (circle one): Accepted OR Rejected
c. (5 pts) What would be the 98% lower confidence limit for the steel yield stress
assuming that the standard deviation of the total population is equal to the
sample deviation?
98% lower confidence limit: ________________ ksi
d. (5 pts) What would be the 95% confidence limit for the steel yield strength based
on an unknown variance?
95% confidence limit: ________________ ksi
as
CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
3 of 7
2. Peck (1940) recorded the shear strength in ksf of 13 clay samples from the Chicago
subway project as follows:
0.35 0.42 0.49 0.70 0.96 0.40 0.43
0.58 0.75 0.41 0.48 0.68 0.87
a. (6 pts) Assuming this data fits a lognormal distribution, estimate l and z using
the method of maximum likelihood
l: ________________
z: ________________
E Be
CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
4 of 7
b. (4 pts) Estimate l and z by calculating the mean and standard deviation (not the
sample mean or sample deviation).
l: ________________
z: ________________
c. (2 pts) How do the parameters from parts a and b compare? Which do you think
is more correct and why?
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Aha Ta
CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
5 of 7
3. During construction of concrete structures, samples are typically cast periodically from
the concrete mix that arrives onsite. Flat plate slabs are cast on formwork (plywood
sheets) supported by shoring. The shoring needs to remain in place until the concrete
cures to the required strength. Then the shoring can be removed and moved upward to
cast the next level.
(courtesy of Ellis Manufacturing, 2023)
Determination of the flat plate slab strength is done by compression testing of the
sample cylinders. Suppose the cylinders are tested and the following compressive
strengths are measured: 3371 3266 3937 4343 3808 3671
a. (5 pts) Determine the 90% two-sided confidence interval of the mean concrete
strength.
she or
CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
6 of 7
Confidence interval: ____________________
b. (5 pts) If your supervisor says that the confidence interval needs to be +/- 350
psi, what would be the percentage of confidence that would be associated with
these tests?
Confidence: ____________________%
Ee Es
CE 525/725 – Applied Statistics
Dr. William J. Kirkham
ã November 4, 2023
HW 5
7 of 7
c. (5 pts) Does this concrete meet the minimum compressive strength of 4000 psi
with a 2% significance level? (Show all work.)
Null hypothesis: ________________________________
Name of test statistic: ________________________________
Value of test statistic: ________________________
Critical value: ________________________
Null hypothesis is (circle one): Accepted OR Rejected
Ba t