Solved: A study was done to determine the impact of two

Chapter 14, Problem 14.11

(choose chapter or problem)

A study was done to determine the impact of two factors, method of analysis and the laboratory doing the analysis, on the level of sulfur content in coal. Twenty-eight coal specimens were randomly assigned to 14 factor combinations, the structure of the experimental units represented by combinations of seven laboratories and two methods of analysis with two specimens per factor combination. The data, expressed in percent of sulfur, are as follows: Method Laboratory 1 2 1 0.109 0.105 0.105 0.108 2 0.129 0.122 0.127 0.124 3 0.115 0.112 0.109 0.111 4 0.108 0.108 0.117 0.118 5 0.097 0.096 0.110 0.097 6 0.114 0.119 0.116 0.122 7 0.155 0.145 0.164 0.160(The data are taken from G. Taguchi, Signal to Noise Ratio and Its Applications to Testing Material, Reports of Statistical Application Research, Union of Japanese Scientists and Engineers, Vol. 18, No. 4, 1971.) (a) Do an analysis of variance and show results in an analysis-of-variance table. (b) Is interaction signicant? If so, discuss what it means to the scientist. Use a P-value in your conclusion. (c) Are the individual main eects, laboratory, and method of analysis statistically signicant? Discuss what is learned and let your answer be couched in the context of any signicant interaction. (d) Do an interaction plot that illustrates the eect of interaction. (e) Do a test comparing methods 1 and 2 at laboratory 1 and do the same test at laboratory 7. Comment on what these results illustrate.