Refer to the American Ceramic Society Bulletin (Feb. 2005) study of the lifetime of an aluminum smelter pot, presented in Exercise 11.143 (p. 646). 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 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 a = .01.

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Brick Apparent Porosity (%) Mean Pore Dlameter (micrometers) A 18.8 18.3 12.0 9.7 16.3 6.9 17.1 7.3 5.3 10.9 16.8 D F 20.4