Twinned drill holes. Refer to the Exploration and Mining Geology (Vol. 18, 2009) study of drill twinned holes, Exercise 8.33 (p. 462). Recall that the drilling of a new hole, or “twin,” next to an earlier drill hole is a traditional method of verifying mineralization grades. The data in the next table represent total amount of heavy minerals (THM) percentages for a sample of 15 twinned holes drilled at a diamond mine in Africa. In Exercise 8.33 you used a confidence interval based on Student’s t-distribution to check for a difference in the true THM means of all original holes and their twin holes drilled at the mine.

a. Explain why the results of the confidence interval may be invalid.

b. What is the appropriate nonparametric test to apply? State H0 and Ha for the test. Location 1st Hole 2nd Hole 1 5.5 5.7 2 11.0 11.2 3 5.9 6.0 4 8.2 5.6 5 10.0 9.3 6 7.9 7.0 7 10.1 8.4 8 7.4 9.0 9 7.0 6.0 10 9.2 8.1 11 8.3 10.0 12 8.6 8.1 13 10.5 10.4 14 5.5 7.0 15 10.0 11.2 Source: Data from Exploration and Mining Geology, Vol. 18, 2009.

c. Compute the difference between the “1st hole” and “2nd hole” measurements for each drilling location.

d. Rank the differences, part

c. e. Compute the rank sums of the positive and negative differences.

f. Use the rank sums, part

e, to conduct the nonparametric test at a = .05. Can the geologists conclude that there is no evidence of a difference in the THM distributions of all original holes and their twin holes drilled at the mine?