Refer to the Chemical Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, Exercise 10.10. You fit a straight-line model relating the mass y (in pounds) of the spill to elapsed time x (in minutes) using the data provided.

a. Find a 90% confidence interval for the true slope of the line. Interpret the result.

b. Conduct a test (at α = .10) 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 10.10

A contract engineer at DuPont Corp. studied the rate at which a spilled volatile liquid will spread across a surface (Chemical Engineering Progress, Jan. 2005). Assume 50 gallons of methanol spills onto a level surface outdoors. The engineer used derived empirical formulas (assuming a state of turbulent-free convection) to calculate the mass (in pounds) of the spill after a period of time ranging from 0 to 60 minutes. The calculated mass values are given in the accompanying table.

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LIQUIDSPILL Time Mass Time Mass (minutes) (pounds) (minutes) (pounds) 6.64 22 1.86 1 6.34 24 1.60 2 6.04 26 1.37 5.47 28 1.17 6 4.94 30 0.98 8 4.44 35 0.60 10 3.98 40 0.34 12 3.55 45 0.17 14 3.15 50 0.06 16 2.79 55 0.02 18 2.45 60 0.00 20 2.14