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.