Extending the life of an aluminum smelter pot. Refer to the American Ceramic Society Bulletin (Feb. 2005) study of the lifetime of an aluminum smelter pot, presented in Exercise.
Extending the life of an aluminum smelter pot. An investigation of the properties of bricks used to line aluminum smelter pots was published in The American Ceramic Society Bulletin (Feb. 2005). Six different commercial bricks were evaluated. The life span of a smelter pot depends on the porosity of the brick lining (the less porosity, the longer is the life); consequently, the researchers measured the apparent porosity of each brick specimen, as well as the mean pore diameter of each brick. The data are given in the next table and saved in the SMELTPOT file.
Brick | Apparent Porosity (%) | Mean Pore Diameter (micrometers) |
A | 18.8 | 12.0 |
B | 18.3 | 9.7 |
C | 16.3 | 7.3 |
D | 6.9 | 5.3 |
E | 17.1 | 10.9 |
F | 20.4 | 16.8 |
Based on Bonadia, P., et al. “Aluminosilicate refractories for aluminum cell linings.” The American Ceramic Society Bulletin , Vol. 84, No. 2, Feb. 2005.
a. Find the least squares line relating porosity ( y ) to mean pore diameter ( x ).
b. Interpret the y -intercept of the line.
c. Interpret the slope of the line.
d. Predict the apparent percentage of porosity for a brick with a mean pore diameter of 10 micrometers.
Since the life of a smelter pot depends on the porosity of the brick lining, the researchers measured the apparent porosity and the mean pore diameter of each of six bricks. The data, saved in the SMELTPOT file, are reproduced in the following table:
a. Rank the apparent porosity values for the six bricks. Then rank the six pore diameter values.
b. Use the ranks from part a to find the rank correlation between apparent porosity ( y ) and mean pore diameter ( x ). Interpret the result.
c. Conduct a test for positive rank correlation. Use α =.01
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