Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.5, Problem 58E
The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. The article “Dependence of Oxidation Stability of Steam Turbine Oil on Base Oil Composition” (J. of the Society of Tribologists and Lubrication Engrs., Oct. 1997: 19–24) reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens.
| TOST | 4200 | 3600 | 3750 | 3675 | 4050 | 2770 |
| RBOT | 370 | 340 | 375 | 310 | 350 | 200 |
| TOST | 4870 | 4500 | 3450 | 2700 | 3750 | 3300 |
| RBOT | 400 | 375 | 285 | 225 | 345 | 285 |
- a. Calculate and interpret the value of the sample
correlation coefficient (as do the article’s authors). - b. How would the value of r be affected if we had let x = RBOT time and y = TOST time?
- c. How would the value of r be affected if RBOT time were expressed in hours?
- d. Construct normal
probability plots and comment. - e. Carry out a test of hypotheses to decide whether RBOT time and TOST time are linearly related.
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The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of
steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens.
TOST
4200
3600
3750
3650
4050
2795
RBOT
370
340
375
310
350
205
TOST
4870
4500
3450
2700
3750
3275
RBOT
400
375
285
225
345
290
(a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.)
The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time
(min) for 12 oil specimens.
TOST
RBOT
4200
370
TOST
RBOT
3575 3750 3700
340
375
315
4050
350
4870 4475 3450
400 375
285
(a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.)
2795
195
2725 3750
220
345
3275
290
Interpret the value of the sample correlation coefficient.
O The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT.
O The value of r indicates that there is a strong, positive linear relationship between TOST and RBOT.
O The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT.
O The value of r indicates that there is a weak, positive linear relationship between TOST and RBOT.
(b) How…
The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.
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