The article “Drying of Pulps in Sprouted Bed: Effect of

Chapter 8, Problem 9E

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The article “Drying of Pulps in Sprouted Bed: Effect of Composition on Dryer Performance” (M. Medeiros, S. Rocha, et al., Drying Technology, 2002:865–881) presents measurements of pH, viscosity (in \(\mathrm{kg} / \mathrm{m} \cdot \mathrm{s}\)), density (in \(\mathrm{g} / \mathrm{cm}^{3}\)), and BRIX (in percent). The following MINITAB output presents the results of fitting the model

     \(\mathrm{pH}=\beta_{0}+\beta_{1} \text { Viscosity }+\beta_{2} \text { Density }+\beta_{3} \text { BRIX }+\varepsilon\)

a. Predict the pH for a pulp with a viscosity of \(1500 \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\), a density of \(1.04 \mathrm{~g} / \mathrm{cm}^{3}\), and a BRIX of 17.5%.

b. If two pulps differ in density by \(0.01 \mathrm{~g} / \mathrm{cm}^{3}\), by how much would you expect them to differ in pH, other things being equal?

c. The constant term \(\beta_{0}\) is estimated to be negative. But pulp pH must always be positive. Is something wrong? Explain.

d. Find a 95% confidence interval for the mean pH of pulps with viscosity \(1200 \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\)s, density \(1.08 \mathrm{~g} / \mathrm{cm}^{3}\), and BRIX 18.0%.

e. Find a 95% prediction interval for the pH of a pulp with viscosity \(1000 \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\), density \(1.05 \mathrm{~g} / \mathrm{cm}^{3}\), and BRIX 19.0%.

f. Pulp A has viscosity 2000, density 1.03, and BRIX 20.0. Pulp B has viscosity 1000, density 1.05, and BRIX 19.0. Which pulp will have its pH predicted with greater precision? Explain.

Equation Transcription:

Text Transcription:

kg/m{cdot}s

g/cm^3

pH=0+1 Viscosity+2 Density+3 BRIX+

1500 kg/m{cdot}s

1.04 g/cm^3

0.01 g/cm^3

beta_0

1200 kg/m{cdot}s

1.08 g/cm^3

1000 kg/m{cdot}s

1.05 g/cm^3