Refer to the Environmental & Engineering Geoscience (Nov. 2012) study of the settlement of structures built on shallow foundations, Exercise 9.46 (p. 462). Recall that actual settlement data (measured in millimeters) for a sample of 13 structures built on a shallow foundation were collected, and these values were compared to settlement predictions made using a formula that accounts for dimension, rigidity, and embedment
depth of the foundation. The data are reproduced in the table. Because it is unlikely that the difference between actual and predicted is normally distributed, the researchers want to make the comparison using a nonparametric procedure.

a. Which nonparametric test should be applied to the data? Why?
b. Specify the null and alternative hypotheses for the test.
c. Compute the difference between actual and predicted settlement values for each of the 13 sampled structures.
d. Rank the absolute values of the differences, part c.
e. Use the ranks, part d, to find the appropriate test statistic.
f. Find the rejection region for the test using a = .01.
g. Make the appropriate conclusion in the words of the problem.

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Predicted Structure Actual 11 11 11 11 3 10 12 4 6. 5 11 10 39 51 9. 23 24 10 269 252 11 4 3 12 82 68 250 264 13