- (2 points) The ANOVA from a randomized complete block experiment output is shown below.
Source DF 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?
- (3 points) An aluminum master alloy manufacturer produces grain refiners in ingot form. The company produces the product 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 impacts 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.
Stirring Rate Furnace
1 2 3 4
5 9 5 6 7
10 15 6 7 10
15 15 7 10 3
20 18 10 4 7
(a) Is there any evidence that stirring rate impacts grain size?
(b) What should the process engineers recommend concerning the choice of stirring rate and furnace for this particular grain refiner if small grain size is desirable?
Sample Solution
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