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: ________________

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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.

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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: ____________________%

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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