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 1.2, Problem 12E
The accompanying summary data on CeO2 particle sizes (nm) under certain experimental conditions was read from a graph in the article “Nanoceria-Energetics of Surfaces, Interfaces and Water Adsorption” (J. of the Amer. Ceramic Soc., 2011: 3992-3999):
3.0−<3.5 | 3.5−<4.0 | 4.0−<4.5 | 4.5−<5.0 | 5.0−<5.5 |
5 | 15 | 27 | 34 | 22 |
5.5−<6.0 | 6.0−<6.5 | 6.5−<7.0 | 7.0−<7.5 | 7.5−<8.0 |
14 | 7 | 2 | 4 | 1 |
- a. What proportion of the observations are less than 5?
- b. What proportion of the observations are at least 6?
- c. Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed? [Note: The investigators fit a lognormal distribution to the data; this is discussed in Chapter 4.]
- d. Construct a histogram with density on the vertical axis and compare to the histogram in (c).
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т
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-0.619
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3.084
0.018
0.306
11.011
0.000
0.272
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3.300
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-0.022
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0.549
XXз
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-1.004
0.349
X>Xз
0.036
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Of the following, which is the best next step in the analysis?
i.
Nothing needs to be done. This model is fine.
Drop x;, x;, and x from the model, and then perform an F test.
iii. Drop…
The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary:
Coefficients:
Estimate
Std. Error
t value
Pr(> |t|)
(Intercept)
−89.010
16.720
−5.324
0.000
Length
0.704
0.049
14.333
0.000
Using this information, give the equation of the least squares regression line.
Chapter 1 Solutions
Probability and Statistics for Engineering and the Sciences
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