Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 9.3, Problem 47E
The article “Slender High-Strength RC Columns Under Eccentric Compression” (Magazine of Concrete Res., 2005: 361–370) gave the accompanying data on cylinder strength (MPa) for various types of columns cured under both moist conditions and laboratory drying conditions.
| Type | ||||||
| 1 | 2 | 3 | 4 | 5 | 6 | |
| M: | 82.6 | 87.1 | 89.5 | 88.8 | 94.3 | 80.0 |
| LD: | 86.9 | 87.3 | 92.0 | 89.3 | 91.4 | 85.9 |
| 7 | 8 | 9 | 10 | 11 | 12 | |
| M: | 86.7 | 92.5 | 97.8 | 90.4 | 94.6 | 91.6 |
| LD: | 89.4 | 91.8 | 94.3 | 92.0 | 93.1 | 91.3 |
a. Estimate the difference in true average strength under the two drying conditions in a way that conveys information about reliability and precision, and interpret the estimate. What does the estimate suggest about how true average strength under moist drying conditions compares to that under laboratory drying conditions?
b. Check the plausibility of any assumptions that underlie your analysis of (a).
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A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 329.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 425.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 389.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 341.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 414.4 441.8 419.9 410.7 473.4 441.2 465.8
USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Ho: M₁ = H₂ = 13 = H4 = 1₂
H₂: all five μ's are unequal
O Ho: My H₂ H3 ‡ M4 # M5
H₂: at least two μ's are equal
O Ho: My # H₂ H3 # H4 # H5
H₂: all five us are equal
=
=
o Hỏi khi là không = 3 = Mà khô
H₂: at least two μ's are unequal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Sum of
Squares
Source
Treatments
Error…
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 315.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 405.1
347.2 361.0 404.5 331.0 348.9 381.7
8:
399.4 366.2 351.0 357.1
409.9 367.3
382.0
10: 353.7 452.9
461.4 433.1
410.6 384.2
362.6
12: 417.4
441.8 419.9 410.7
473.4 441.2
465.8
n USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Ho: H1# H2 # Hz# H4# H5
H: at least two µ's are equal
O Ho: H1 = H2 = H3= H4= H5
H: at least two u's are unequal
O Ho: H1 # H2 # Hz# H4# Hs
H: all five u's are equal
O Ho: H1 = H2 = Hz3 = H4= Hs
H: all five u,'s are unequal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Degrees of
freedom
Sum of
Squares
Mean
Source…
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4:
323.2
409.5
311.0
326.5
316.8
349.8
309.7
6:
423.1
347.2
361.0
404.5
331.0
348.9
381.7
8:
393.4
366.2
351.0
357.1
409.9
367.3
382.0
10:
362.7
452.9
461.4
433.1
410.6
384.2
362.6
12:
418.4
441.8
419.9
410.7
473.4
441.2
465.8
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: all five ?i's are equal
Test the relevant hypotheses using analysis of variance with ? = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Source
Degrees offreedom
Sum…
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Probability and Statistics for Engineering and the Sciences
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