Twinned drill holes. A traditional method of verifying mineralization grades in mining is to drill twinned holes, i.e., the drilling of a new hole, or “twin,” next to an earlier drillhole. The use of twinned drill holes was investigated in Exploration and Mining Geology (Vol. 18, 2009).

Geologists use data collected at both holes to estimate the total amount of heavy minerals (THM) present at the drilling LO5 site. The data in the next table (based on information provided in the journal article) represent THM percentages for a sample of 15 twinned holes drilled at a diamond mine in Africa. The geologists want to know if there is any evidence of a difference in the true THM means of all original holes and their twin holes drilled at the mine.

a. Explain why the data should be analyzed as paired differences.

b. Compute the difference between the “1st hole” and

“2nd hole” measurements for each drilling location.

c. Find the mean and standard deviation of the differences, part b.

d. Use the summary statistics, part

c, to find a 90% confidence interval for the true mean difference (“1st hole”
minus “2nd hole”) in THM measurements.

e. Interpret the interval, part

d. Can the geologists conclude that there is no evidence of a difference in the true THM means 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