Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 13.2, Problem 21E
Mineral mining is one of the most important economic activities in Chile. Mineral products are frequently found in saline systems composed largely of natural nitrates. Freshwater is often used as a leaching agent for the extraction of nitrate, but the Chilean mining regions have scarce freshwater resources. An alternative leaching agentis seawater. The authors of “Recovery of Nitrates from Leaching Solutions Using Seawater” (Hydrometallurgy, 2013: 100–105) evaluated the recovery of nitrate ions from discarded salts using freshwater and seawater leaching agents. Here is data on x 5 leaching time (h) and y 5 nitrate extraction percentage (seawater):
| x | 25.5 | 31.5 | 37.5 | 43.5 | 49.5 | 55.5 |
| y | 26.4 | 40.1 | 50.2 | 57.4 | 62.7 | 67.3 |
| x | 61.5 | 67.5 | 73.5 | 79.5 | 85.5 | 91.5 |
| y | 71.4 | 74.7 | 77.8 | 80.3 | 82.3 | 84.1 |
| x | 97.5 | 103.5 | 109.5 | 115.5 | 121.5 | 127.5 |
| y | 85.5 | 86.6 | 87.9 | 89.0 | 89.9 | 90.6 |
| x | 133.5 | 139.5 | 145.5 | 151.5 | 157.5 | |
| y | 91.2 | 91.8 | 92.3 | 92.8 | 93.3 |
a. Construct a
b. Construct a scatterplot of y versus x’ = 1/x and speculate on the value of r2 after fitting the simple linear regression model to the transformed data. c. Obtain a 95% prediction interval for nitrogen extraction percentage when leaching time = 100 h.
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4. A study to assess the capability of subsurface flow wetland systems to remove
biochemical oxygen demand (BOD) and various other chemical constituents
resulted in the accompanying data on z = BOD mass loading (kg/ha/d) and y
= BOD mass removal (kg/ha/d) ("Subsurface Flow Wetlands-A Performance
Evaluation." Water Envir. Res., 1995: 244-247).
x
Y
11
8
13 16 27
10 11 16
142
35 38 44 103
30
90
75
31 30
26 21
n = 10; Σ | n = 450; Σα" = 37653; Σy = 318; Σ y = 17244; Σ =y = 25344
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Chapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
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