Refer to The American Ceramic Society Bulletin (Feb. 2005) evaluation of commercial bricks used in smelter pots, Exercise 10.9. You fit a straight-line model relating the apparent porosity y (in percent) of the brick to mean pore diameter x (in micrometers) using the data provided.

a. Find a 95% confidence interval for the true slope of the line. Interpret the result.

b. Conduct a test (at α = .05) to determine if the true slope of the line differs from 0.

c. Demonstrate that the two inferences, parts a and b, give the same information on the utility of the straight-line model.

Data from Exercise 10.9

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     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.

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SMELTPOT Apparent Porosity (%) Mean Pore Diameter (micrometers) Brick A 18.8 12.0 В 18.3 9.7 C 16.3 7.3 6.9 5.3 E 17.1 10.9 F 20.4 16.8