An experiment was conducted to investigate the effect of four factorstemperature T1

Chapter 11, Problem 11.74

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An experiment was conducted to investigate the effect of four factorstemperature T1, pressure P, catalyst C, and temperature T2on the yield Y of a chemical. a The values (or levels) of the four factors used in the experiment are shown in the accompanying table. If each of the four factors is coded to produce the four variables x1, x2, x3, and x4, respectively, give the transformation relating each coded variable to its corresponding original. T1 x1 P x2 C x3 T2 x4 50 1 10 1 1 1 100 1 70 1 20 1 2 1 200 1 b Fit the linear model Y = 0 + 1x1 + 2x2 + 3x3 + 4x4 + to the following table of data. x4 +1 1 x3 x3 1 1 1 1 1 x2 1 22.2 24.5 24.4 25.9 x1 1 19.4 24.1 25.2 28.4 1 22.1 19.6 23.5 16.5 +1 x2 1 14.2 12.7 19.3 16.0 c Do the data present sufficient evidence to indicate that T1 contributes information for the estimation of Y ? Does P? DoesC? Does T2? (Test the hypotheses, respectively, that 1 = 0, 2 = 0, 3 = 0, and 4 = 0.) Give bounds for the p-value associated with each test. What would you conclude if you used = .01 in each case?

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