PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
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Chapter 12.3, Problem 36E
Misi (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. The article “Variables Affecting Mist Generaton from Metal Removal Fluids” (Lubrication Engr., 2002: 10–17) gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 μm (mg/m3):
| x | 89 | 177 | 189 | 354 | 362 | 442 | 965 |
| y | .40 | .60 | .48 | .66 | .61 | .69 | .99 |
- a. The investigators performed a simple linear
regression analysis to relate the two variables. Does ascatterplot of the data support this strategy? - b. What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist?
- c. The investigators were particularly interested in the impact on mist of increasing velocity from 100 to 1000 (a factor of 10 corresponding to the difference between the smallest and largest x values in the sample). When x increases in this way, is there substantial evidence that the true average increase in y is less than .6?
- d. Estimate the true average change in mist associated with a 1 cm/see increase in velocity, and do so in a way that conveys information about precision and reliability.
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Chapter 12 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
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