Refer to the Environmental Geology (Vol. 58, 2009) simulation study of how far a block from a collapsing rock wall will bounce down a soil slope, Exercise 2.29. Rebound lengths (in meters) were estimated for 13 rock bounces. The data are repeated in the table. Descriptive statistics for the rebound lengths are shown on the accompanying SAS printout. Consider a test of hypothesis for the variation in rebound lengths for the theoretical population of rock bounces from the collapsing rock wall. In particular, a geologist wants to determine if the variance differs from 10 m².

a. Define the parameter of interest.
b. Specify the null and alternative hypothesis.
c. Compute the value of the test statistic.
d. Determine the rejection region for the test using α = .10.
e. Make the appropriate conclusion.
f. What condition must be satisfied in order for the inference, part e, to be valid?

Data from Exercise 2.29

In Environmental Geology (Vol. 58, 2009) computer simulation was employed to estimate how far a block from a collapsing rock wall will bounce—called rebound length—down a soil slope. Based on the depth, location, and angle of block-soil impact marks left on the slope from an actual rock fall, the following 13 rebound lengths (meters) were estimated. Compute the mean and median of the rebound lengths and interpret these values.

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ROCKFALL 10.94 13.71 11.38 7.26 17.83 11.92 11.87 5.44 13.35 4.90 5.85 5.10 6.77