Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 9.3, Problem 11E
a.
To determine
Find all the main and interaction effects.
b.
To determine
Construct an ANOVA table and the find the
c.
To determine
Explain whether the additive model is plausible.
d.
To determine
Check whether the effects of material on coefficient of friction can be described by the main effects of material.
e.
To determine
Check whether the effects of neck length on coefficient of friction can be described by the main effects of neck length. If so, interpret the main effects by multiple comparisons at the 5% level. If not explain the reason.
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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:
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…
In 58 specimens of a new aluminum alloy that is developed as a material for the next generation of aircraft, the compressive strength was measured, obtaining the following results:
66.4 67.7 68.0 68.0 69.5 70.4 71.6 72.9 69.0 69.169.2 69.3 69.3 69.5 70.3 71.5 72.7 68.9 69.9 70.070.0 70.1 70.2 70.3 71.3 72.6 68.8 69.8 70.8 70.971.0 71.1 71.2 71.3 72.4 68.6 69.8 70.6 71.8 71.871.9 72.1 72.2 72.3 68.4 69.7 70.6 71.7 73.3 73.574.2 74.5 75.3 68.3 69.6 70.5 71.6 73.1
a. Find a 95% confidence interval for the mean strength of the aluminum alloy.b. If you want to test Ho: Mu = 72 against H1: Mu different from 72 with a significance level of 0.05, what is the probability of a type II error for Mu = 71?
In 58 specimens of a new aluminum alloy that is developed as a material for the next generation of aircraft, the compressive strength was measured, obtaining the following results:
66.4 67.7 68.0 68.0 69.5 70.4 71.6 72.9 69.0 69.169.2 69.3 69.3 69.5 70.3 71.5 72.7 68.9 69.9 70.070.0 70.1 70.2 70.3 71.3 72.6 68.8 69.8 70.8 70.971.0 71.1 71.2 71.3 72.4 68.6 69.8 70.6 71.8 71.871.9 72.1 72.2 72.3 68.4 69.7 70.6 71.7 73.3 73.574.2 74.5 75.3 68.3 69.6 70.5 71.6 73.1
a. Find a 95% confidence interval for the mean resistance of thealuminium alloy.b. If you want to test Ho:Mu =72 against H1: Mu different from 72 with a significance level of 0.05, what is the probability of a type II error for Mu= 71?
Chapter 9 Solutions
Statistics for Engineers and Scientists
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Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Refer to Exercise 12. a. Compute the quantity...Ch. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - The following MINITAB output presents a power...Ch. 9.2 - Exercises for Section 9.2 1.The article Organic...Ch. 9.2 - The article Optimum Design of an A-pillar Trim...Ch. 9.2 - Prob. 3ECh. 9.2 - Refer to Exercise 2 in Section 9.1. a.Use the...Ch. 9.2 - Refer to Exercise 13 in Section 9.1. a. Use the...Ch. 9.2 - Refer to Exercise 1 in Section 9.1. A scientist...Ch. 9.2 - Refer to Exercise 13 in Section 9.1. A...Ch. 9.2 - Refer to Exercise 3 in Section 9.1. a. Use the...Ch. 9.2 - Refer to Exercise 5 in Section 9.1. a. Use the...Ch. 9.2 - Refer to Exercise 9 in Section 9.1. a. Use the...Ch. 9.2 - Refer to Exercise 16 in Section 9.1. a. Use the...Ch. 9.2 - Refer to Exercise 18 in Section 9.1. a. Use the...Ch. 9.2 - In an experiment to determine the effect of...Ch. 9.2 - In an experiment to determine the effect of curing...Ch. 9.2 - Prob. 15ECh. 9.2 - For some data sets, the F statistic will reject...Ch. 9.3 - To assess the effect of piston ring type and oil...Ch. 9.3 - A machine shop has three machines used in...Ch. 9.3 - An experiment to determine the effect of mold...Ch. 9.3 - The effect of curing pressure on bond strength was...Ch. 9.3 - The article Change in Creep Behavior of Plexiform...Ch. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Adding glass panicles to clay brick may improve...Ch. 9.3 - The article Application of Radial Basis Function...Ch. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - The article Anodic Fenton Treatment of Treflan MTF...Ch. 9.3 - Refer to Exercise 12. The treatments with a...Ch. 9.3 - The article Use of Taguchi Methods and Multiple...Ch. 9.3 - The article T-Bracing for Stability of Compression...Ch. 9.3 - The article referred to in Exercise 15 also...Ch. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - The article Cellulose Acetate Microspheres...Ch. 9.4 - Recycling newsprint is important in reducing...Ch. 9.4 - A study was done to see which of four machines is...Ch. 9.4 - Prob. 3ECh. 9.4 - Three different corrosion-resistant coatings are...Ch. 9.4 - The article Genotype-Environment Interactions and...Ch. 9.4 - The article Sprinkler Technologies, Soil...Ch. 9.4 - The article Bromate Surveys in French Drinking...Ch. 9.4 - The article Multi-objective Scheduling Problems:...Ch. 9.4 - You have been given the task of designing a study...Ch. 9.4 - An engineering professor wants to determine which...Ch. 9.5 - Prob. 1ECh. 9.5 - Give an example of a factorial experiment in which...Ch. 9.5 - Prob. 3ECh. 9.5 - The article Efficient Pyruvate Production by a...Ch. 9.5 - The article cited in Exercise 4 also investigated...Ch. 9.5 - A metal casting process for the production of...Ch. 9.5 - The article An Investigation into the Ball...Ch. 9.5 - In a 2p design with one replicate per treatment,...Ch. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - The article Factorial Design for Column Rotation...Ch. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9 - The article Gypsum Effect on the Aggregate Size...Ch. 9 - Prob. 2SECh. 9 - Prob. 3SECh. 9 - Prob. 4SECh. 9 - Prob. 5SECh. 9 - Prob. 6SECh. 9 - Prob. 7SECh. 9 - The article Case Study Based Instruction of DOE...Ch. 9 - The article Combined Analysis of Real-Time...Ch. 9 - Vermont maple sugar producers sponsored a testing...Ch. 9 - Prob. 11SECh. 9 - Prob. 12SECh. 9 - Prob. 13SECh. 9 - The article Enthalpies and Entropies of Transfer...Ch. 9 - Prob. 15SECh. 9 - Prob. 16SECh. 9 - The article Factorial Experiments in the...Ch. 9 - The Williamsburg Bridge is a suspension bridge...Ch. 9 - Prob. 19SECh. 9 - In the article Nitrate Contamination of Alluvial...Ch. 9 - The article Factorial Experiments in the...Ch. 9 - Prob. 22SECh. 9 - Prob. 23SECh. 9 - Prob. 24SE
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