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Completely Randomized and Randomized Complete Block Designs

For each of the following problems you are to provide the following:

a) The experimental design structure (CRD, RCBD).
b) The null and research hypothesis, test statistic and all important (necessary) summary statistics, rejection region and conclusion.
c) Based on the results of the analysis (part b), could you have made a type I error or a type II error? Explain why you could have committed the error.
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1. The urinary fluoride concentration (ppm) was determined for 11 randomly chosen livestock both at the beginning of and in the middle of their grazing period in a region which has previously been exposed to fluoride pollution ("Fluoride Pollution Caused by a Brickworks in the Flemish Countryside of Belgium," Int. J. Environmental Studies, 1978, pp. 245-252).

Subject: 1 2 3 4 5 6 7 8 9 10 11
Beginning: 24.7 46.1 18.5 29.5 26.3 33.9 23.1 20.7 18.0 19.3 23.0
Middle: 12.4 14.1 7.6 9.6 19.7 10.6 9.1 11.5 13.3 8.3 15.0

Do these data suggest a difference between beginning and middle grazing period fluoride levels?
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2.Borderline and mildly retarded children attending a hospital developmental evaluation clinic were divided into two groups on the basis of the presence or absence of a probable aetiological factor causing the retardation. Blood-lead concentration was measured for each child, yielding the following data:

Aetiology Unknown: 25.5 23.2 27.6 24.3 26.1 25.0
Probable Aetiology: 21.2 19.8 20.3 21.0 19.6

Does the data indicate any difference in true average blood-lead concentration for the two types of children?

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Solution Preview

Please see the attached files. Hope these help.

For each of the following problems you are to provide the following:

a) The experimental design structure (CRD, RCBD).
b) The null and research hypothesis, test statistic and all important (necessary) summary statistics, rejection region and conclusion.
c) Based on the results of the analysis (part b), could you have made a type I error or a type II error? Explain why you could have committed the error.
-----------------------
1. The urinary fluoride concentration (ppm) was determined for 11 randomly chosen livestock both at the beginning of and in the middle of their grazing period in a region which has previously been exposed to fluoride pollution ("Fluoride Pollution Caused by a Brickworks in the Flemish Countryside of Belgium," Int. J. Environmental Studies, 1978, pp. 245-252).

Subject: 1 2 3 4 5 6 7 8 9 10 11
Beginning: 24.7 46.1 18.5 29.5 26.3 33.9 23.1 20.7 18.0 19.3 23.0
Middle: ...

Solution Summary

Word and Excel files attached show how to answer two questions about block experiment design using examples of retarded children and fluoride concentration in urine.

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