Twinned drill holes. Refer to the Exploration and Mining Geology (Vol. 18, 2009) study of drill twinned holes, Exercise 8.33 (p. 455). 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 H0andH2for the test.
- 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, parte, to conduct the nonparametric test at α = .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?
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. |
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