Chapter 11, Problem 11.108ACB

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 (February 2005). Six different commercial bricks were evaluated. The life length of a smelter pot depends on the porosity of the brick lining (the less porosity, the longer 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 accompanying table.

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

1. a. Find the least squares line relating porosity (y) to mean pore diameter (x).
2. b. Interpret the y-intercept of the line.
3. c. Interpret the slope of the line.
4. d. Conduct a test to determine whether porosity (y) and diameter (x) are positively linearly related. Use α = .01.