Statistics / Statistics for Engineers and Scientists 4 / Chapter 9 / Problem 6

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

The article Stability of Silico-Ferrite of Calcium and Aluminum (SFCA) in Air-Solid

Chapter 9, Problem 6

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The article “Stability of Silico-Ferrite of Calcium and Aluminum (SFCA) in Air-Solid Solution Limits Between $1240^\circ \mathrm C$ and $1390^\circ \mathrm C$ and Phase Relationships within the $\mathrm{Fe}_{2} \mathrm{O}_{3}\text -\mathrm{CaO}\text -\mathrm{Al}_{2} \mathrm{O}_{3}\text -\mathrm{SiO}_{2}$ (FCAS) System” (T. Patrick and M. Pownceby, Metallurgical and Materials Transactions B, 2002:79–90) investigates properties of silico-ferrites of calcium and aluminum (SFCA). The data in the following table present the ratio of the weights of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ and CaO for SFCA specimens with several different weight percents of $\mathrm{Al}_{2} \mathrm{O}_{3}$ and $\mathrm{C}_{4} \mathrm{S}_{3}$.

a. Estimate all main effects and interactions.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Do the data indicate that there are any interactions between the weight percent of $\mathrm{Al}_{2} \mathrm{O}_{3}$ and the weight percent of $\mathrm{C}_{4} \mathrm{S}_{3}$? Explain.

d. Do the data convincingly demonstrate that the $\mathrm{Fe}_{2}\mathrm{O}_{3}\mathrm{/CaO}$ ratio depends on the weight percent of $\mathrm{Al}_{2} \mathrm{O}_{3}$? Explain.

e. Do the data convincingly demonstrate that the $\mathrm{Fe}_{2} \mathrm{O}_{3}\mathrm{/CaO}$ ratio depends on the weight percent of $\mathrm{C}_{4} \mathrm{S}_{3}$? Explain.

Equation Transcription:

$124{0}^{o}C$