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Homework answers / question archive / 4point1) The ANOVA from a randomized complete block experiment output is shown below

4point1) The ANOVA from a randomized complete block experiment output is shown below

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4point1) The ANOVA from a randomized complete block experiment output is shown below. 
Source OF SS MS F P Treatment 4 1010.56 ? 29.84 ? Block ? ? 64.765 ? ? Error 20 169.33 ? Total 29 1503.71 
(a) Fill in the blanks. You may give bounds on the P-value. (b) How many blocks were used in this experiment? (c) What conclusions can you draw? 

 

4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in 5-gallon milk containers. The analysis is done in a laboratory, and only three trials can be run on any day. Because days could represent a potential source of variability, the experimenter decides to use a randomized block design. Observations are taken for four days, and the data are shown here. Analyze the data from this experiment (use a = 0.05) and draw conclusions. 
Days Solution 1 2 3 4 1 13 22 18 39 2 16 24 17 44 3 5 4 1 22 

 

4.14. An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the prod-uct in four furnaces. Each furnace is known to have its own unique operating characteristics, so any experiment run in the foundry that involves more than one furnace will consider furnaces as a nuisance variable. The process engineers suspect that stirring rate affects the grain size of the product. Each furnace can be run at four different stirring rates. A randomized block design is run for a particular refiner, and the resulting grain size data is as follows. 
Furnace Stirring Rate (rpm) 1 2 3 4 5 8 4 5 6 10 14 5 6 9 15 14 6 9 2 20 17 9 3 6 
(a) Is there any evidence that stirring rate affects grain size? (b) Graph the residuals from this experiment on a normal probability plot. Interpret this plot. (c) Plot the residuals versus furnace and stirring rate. Does this plot convey any useful information? (d) What should the process engineers recommend con-cerning the choice of stirring rate and furnace for this particular grain refiner if small grain size is desirable? 

4.23. An industrial engineer is investigating the effect of four assembly methods (A, B, C, D) on the assembly time for a color television component. Four operators are selected for the study. Furthermore, the engineer knows that each assem-bly method produces such fatigue that the time required for the last assembly may be greater than the time required for the first, regardless of the method. That is, a trend develops in the required assembly time. To account for this source of variabil-ity, the engineer uses the Latin square design shown below. Analyze the data from this experiment (a = 0.05) and draw appropriate conclusions. 
Order of Operator Assembly 1 2 3 4 1 C = 10 D = 14 A = 7 B = 8 2 B = 7 C = 18 D = 11 A = 8 3 A = 5 B = 10 C = 11 D=9 4 D = 10 A = 10 B = 12 C = 14 
 

4.42. Seven different hardwood concentrations are being studied to determine their effect on the strength of the paper produced. However, the pilot plant can only produce three runs each day. As days may differ, the analyst uses the bal-anced incomplete block design that follows. Analyze the data from this experiment (use a = 0.05) and draw conclusions. 
Hardwood Concentration (%) Days 1 2 3 4 2 4 6 8 10 12 114 126 141 120 137 117 129 145 120 149 150 14 136 Hardwood Days Concentration (%) 5 6 7 2 120 117 4 119 6 134 8 10 143 12 118 123 14 130 127 
 

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