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# The article "Sprinkler Technologies, Soil Infiltration,

ISBN: 9780073401331 38

## Solution for problem 6E Chapter 9.4

Statistics for Engineers and Scientists | 4th Edition

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Problem 6E

The article "Sprinkler Technologies, Soil Infiltration, and Runoff” (D. DeBoer and S. Chu, Journal of Irrigation and prainage Engineering. 2001:234-239) presents a study of the runoff depth (in mm) for various sprinkler types. Each 0f four sprinklers was tested on each of four days, with two replications per day (there were three replications on a few of the days; these are omitted). It is of interest to detennine whether runotf depth varies with sprinkler type; variation from one day to another is not of interest. The data are presented in the following table.

 Sprinkler Day 1 Day 2 Day 3 Day4 A 8.3 5.5 7.8 4.5 10.7 9.8 10.6 6.6 B 6.5 9.5 3.7 3.6 7.7 10.6 3.6 6.7 C 1.8 1.2 0.5 0.3 1.7 1.9 2.2 2.1 D 0.7 0.8 0.1 0.5 0.1 0.5 0.3 0.5

a. Identify the blocking factor and the treatment factor.

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

c. Are the assumptions of a randomized complete block design met? Explain.

d. Can you conclude that there are differences in mean runoff depth between some pairs of sprinklers? Explain.

e. Which pairs of sprinklers, if any, can you conclude, at the 5% level, to have differing mean runoff depths?

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