Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9.5, Problem 65E
The article “Enhancement of Compressive Properties of Failed Concrete Cylinders with Polymer Impregnation” (J. of Testing and Evaluation, 1977: 333–337) reports the following data on impregnated compressive modulus (psi 3 106) when two different polymers were used to repair cracks in failed concrete.
| Epoxy | 1.75 | 2.12 | 2.05 | 1.97 |
| MMA prepolymer | 1.77 | 1.59 | 1.70 | 1.69 |
Obtain a 90% CI for the ratio of variances by first using the method suggested in the text to obtain a general confidence interval formula.
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Consider the following summary data on the modulus of elasticity (✕ 106 psi) for lumber of three different grades.
Grade
J
xi.
si
1
9
1.61
0.21
2
9
1.55
0.25
3
9
1.44
0.23
Use this data and a significance level of 0.01 to test the null hypothesis of no difference in mean modulus of elasticity for the three grades. Calculate the test statistic. (Round your answer to two decimal places.)
f =
What can be said about the P-value for the test?
P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001
What can you conclude?
Reject H0. At least two of the three grades appear to differ significantly. Reject H0. The three grades do not appear to differ significantly. Fail to reject H0. The three grades do not appear to differ significantly. Fail to reject H0. At least two of the three grades appear to differ significantly.
ONLY THE LAST ONE
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
5.9
7.2
7.3
6.3
8.1
6.8
7.0
7.5
6.8
6.5
7.0
6.3
7.9
9.0
8.4
8.7
7.8
9.7
7.4
7.7
9.7
8.2
7.7
11.6
11.3
11.8
10.7
The data below give accompanying strength observations for cylinders.
6.5
5.8
7.8
7.1
7.2
9.2
6.6
8.3
7.0
8.3
7.8
8.1
7.4
8.5
8.9
9.8
9.7
14.1
12.6
11.9
Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2.
(a) Use rules of expected value to show that
X − Y
is an unbiased estimator of μ1 − μ2.
E(X − Y) = E(X) − E(Y) = μ1 − μ2
E(X − Y) =
E(X) − E(Y)
2
= μ1 − μ2
E(X − Y) = nm
E(X) − E(Y)
= μ1 − μ2
E(X −…
The article “Monte Carlo Simulation—Tool for Better Understanding of LRFD” (J. of Structural Engr., 1993:1586–1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed with a mean of 50.2 ksi and a standard deviation of 3.8 ksi.. What yield strength separates the strongest 5% from the others? (Use 2 decimal places) Show the area of interest in the density curve.
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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