Large highwall failures at a strip mine in Queensland, Australia, occur by the sliding of soft, black

Question:

Large highwall failures at a strip mine in Queensland, Australia, occur by the sliding of soft, black bands of clay, called black clay planes, near the base of the highwall. A study was conducted to determine whether the chemical and mineralogical properties of the black clay planes are similar to mudstone (Engineering Geology, Oct. 1985). Black clay and mudstone specimens were randomly selected at each of three randomly selected sites within the siltstone faces in the ramp area of the mine. The densities of the specimens (in kilograms per cubic meter) are recorded in the table. An SAS printout of the nested ANOVA follows.

a. How many first-stage observations were included in the sample?

b. How many second-stage units were selected per first stage unit?

c. Give the total number of observations obtained in the sample.

d. Write the probabilistic model for this sampling design.

e. Find estimates of σ_α² = 0 and σ² on the printout.

f. Conduct a test to determine whether the variation in black clay and mudstone specimen densities between sites exceeds the variation within sites. Use α = .10.