Consider the data analyzed in Examples 12.2 and 12.3.

1. a Assuming that both the methods used to analyze the samples worked reasonably well, why do you think that the observations on the two halves of each ore sample will be positively correlated?
2. b Do you think that we should have taken independent observations using the two methods, or should we have conducted the paired analysis contained in the text? Why?

EXAMPLE 12.2 We wish to compare two methods for determining the percentage of iron ore in ore samples. Because inherent differences in the ore samples would be likely to contribute unwanted variability in the measurements that we observe, a matched-pairs experiment was created by splitting each of 12 ore samples into two parts. One-half of each sample was randomly selected and subjected to method 1; the other half was subjected to method 2. The results are presented in Table 12.1. Do the data provide sufficient evidence that method 2 yields a higher average percentage than method 1? Test using α = .05.

EXAMPLE 12.3 Use the data from Example 12.2 to form a 95% confidence interval for the difference in mean percentage readings using methods 1 and 2.