J. Vuorinen carried out a series of experiments to gather information on the coefficient of permeability of concrete (Magazine of Concrete Research, Sept. 1985). In one experiment, the outflow of water from the pores of a concrete specimen after it had been under saturating water pressure for a period of time was recorded for different combinations of concrete permeability and porosity. The resulting water quantities after different lapses of time for one permeability–porosity combination are given in the table.

a. According to Vuorinen, “the quantity of water discharged is approximately in linear relationship with the square root of time” for most of the permeability–porosity combinations. Fit the following model to the data in the table:

E(w) = α₀ + α√t

b. Is there sufficient evidence to indicate that quantity of water outflow and the square root of time are linearly related? Test using α = .10.

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CONPERM1 Time Water Outflow w, t, seconds grams per cylinder 201 3.88 325 4.93 525 6.42 775 7.80 975 8.72 1,200 9.60