Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.1, Problem 1E
The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).
| Temp. | 170 | 172 | 173 | 174 | 174 | 175 | 176 |
| Ratio | .84 | 1.31 | 1.42 | 1.03 | 1.07 | 1.08 | 1.04 |
| Temp. | 177 | 180 | 180 | 180 | 180 | 180 | 181 |
| Ratio | 11.80 | 1.45 | 1.60 | 1.61 | 2.13 | 2.15 | .84 |
| Temp. | 181 | 182 | 182 | 182 | 182 | 184 | 184 |
| Ratio | 11.43 | .90 | 1.81 | 1.94 | 2.68 | 1.49 | 2.52 |
| Temp. | 185 | 186 | 188 |
| Ratio | 13.00 | 1.87 | 3.08 |
- a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.
- b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.
- c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.
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The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).Temp. 170 172 173 174 174 175 176Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04Temp. 177 180 180 180 180 180 181Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84Temp. 181 182 182 182 182 184 184Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52Temp. 185 186 188Ratio 3.00 1.87 3.08a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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