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 11.4, Problem 38E
The accompanying data resulted from an experiment to study the nature of dependence of welding current on three factors: welding voltage, wire feed speed, and tip-to-workpiece distance. There were two levels of each factor (a 23 experiment) with two replications per combination of levels (the averages across replications agree with values given in the article “A Study on Prediction of Welding Current in Gas Metal Arc Welding,” J. Engr. Manuf., 1991: 64–69). The first two given numbers are for the treatment (1), the next two for a, and so on in standard order: 200.0, 204.2, 215.5, 219.5, 272.7, 276.9, 299.5, 302.7, 166.6, 172.6, 186.4, 192.0, 232.6, 240.8, 253.4, 261.6.
- a. Verify that the sums of squares are as given in the accompanying ANOVA table from Minitab.
- b. Which effects appear to be important, and why?
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a. Decide whether you can reasonably apply the regression t-test. If so, then also do part (b).
b. Decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.
Body Fat. In the paper “Total Body Composition by Dual- Photon (153 Gd) Absorptiometry” (American Journal of Clinical Nutrition, Vol. 40, pp. 834–839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured for percentage of body fat, using dual-photon absorptiometry. Each adult’s age and percentage of body fat are shown on the WeissStats site.
a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).
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An article described an experiment in which observations on various characteristics were made using minichambers of three
different types: (1) cooler (PVC frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames
covered with plastic). One of the article's authors kindly supplied the accompanying data on the difference between air and soil
temperatures (°C).
Cooler
1.59
1.43
1.88
1.26
1.91
1.86
1.90
1.57
1.79
1.72
2.41
2.34
0.94
1.34
1.76
Control
1.92
2.00
2.19
1.12
1.78
1.84
2.45
2.03
1.52
0.49
1.90
Warmer
2.57
2.60
1.93
1.58
2.30
0.84
2.65
0.15
2.74
2.53
2.13
2.86
2.31
1.91
(a) Compare measures of center for the three different samples.
Cooler X = 1.76
Control
X =
1.90
Warmer X = 2.305
(b) Calculate the standard deviations for the three different samples. (Round your answers to three decimal places.)
Cooler
S = 0.395
Control
S = 0.522
Warmer S = 0.772
X
x
Interpret and compare the standard deviations for the three different samples.
Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 11.1 - An experiment was carried out to investigate the...Ch. 11.1 - Four different coatings are being considered for...Ch. 11.1 - Prob. 3ECh. 11.1 - In an experiment to see whether the amount of...Ch. 11.1 - In an experiment to assess the effect of the angle...Ch. 11.1 - A particular county employs three assessors who...Ch. 11.1 - Prob. 7ECh. 11.1 - The paper Exercise Thermoregulation and...Ch. 11.1 - The article The Effects of a Pneumatic Stool and a...Ch. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - The power curves of Figures 10.5 and 10.6 can be...Ch. 11.2 - In an experiment to assess the effects of curing...Ch. 11.2 - Prob. 17ECh. 11.2 - The accompanying data resulted from an experiment...Ch. 11.2 - A two-way ANOVA was carried out to assess the...Ch. 11.2 - The article Fatigue Limits of Enamel Bonds with...Ch. 11.2 - In an experiment to investigate the effect of...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.3 - The output of a continuous extruding machine that...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Nickel titanium (NiTi) shape memory alloy (SMA)...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - The article The Responsiveness of Food Sales to...Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.4 - The accompanying data resulted from an experiment...Ch. 11.4 - The accompanying data resulted from a 23...Ch. 11.4 - In a study of processes used to remove impurities...Ch. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - a. In a 24 experiment, suppose two blocks are to...Ch. 11.4 - a. An experiment was carried out to investigate...Ch. 11.4 - Prob. 46ECh. 11.4 - a. In a seven-factor experiment (A,, G), suppose a...Ch. 11.4 - The article Applying Design of Experiments to...Ch. 11 - The results of a study on the effectiveness of...Ch. 11 - Prob. 51SECh. 11 - Prob. 52SECh. 11 - In an automated chemical coating process, the...Ch. 11 - Coal-fired power plants used in the electrical...Ch. 11 - Impurities in the form of iron oxides lower the...Ch. 11 - Factorial designs have been used in forestry to...Ch. 11 - Prob. 57SECh. 11 - Prob. 58SECh. 11 - The bond strength when mounting an integrated...Ch. 11 - Prob. 60SECh. 11 - Prob. 61SE
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