Permeability of sandstone during weathering. Refer to the Geographical Analysis (Vol. 42, 2010) study of the permeability of sandstone exposed to the weather, Exercise 2.69 (p. 91). Recall that blocks of sandstone were cut into 300 equal-sized slices and the slices randomly divided into three groups of 100 slices each. Slices in group A were not exposed to any type of weathering; slices in group B were repeatedly sprayed with a 10% salt solution (to simulate wetting by driven rain) under temperate conditions; and slices in group C were soaked in a 10% salt solution and then dried (to simulate blocks of sandstone exposed during a wet winter and dried during a hot summer). All sandstone slices were then tested for permeability, a measure of pressure decay in milliDarcies (mD). The data for the study (simulated) are saved in the SAND file.

a. Write a model for mean permeability, E(y), as a function of sandstone group (A, B, or C).

b. Measures of central tendency for the permeability measurements of each sandstone group are displayed in the MINITAB printout below. Use this information to estimate the b parameters of the model, part a.

c. Fit the model, part

a, to the data in the SAND file. Use the output to verify your b estimates in part b.

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MINITAB Output for Exercise 12.98 Descriptive Statistics: PermA, PermB, PermC N for Variable PernA N Mean Median 100 73.62 70.45 Mode Mode 59.9, 60, 60.1, 60.4 2 PernB PermC 100 128.54 139.30 146.4, 146.6, 147.9, 148.3 100 83.07 78.65 3 70.9 3 The data contain at least five mode values. Only the smallest four are shown.