The diameter of a ball bearing was measured by 12 inspectors, each using two different kinds of calipers. The results are as follows:

Inspector Caliper 1 Caliper 2 1 0.265 0.264 2 0.265 0.265 3 0.266 0.264 4 0.267 0.266 5 0.267 0.267 6 0.265 0.268 7 0.267 0.264 8 0.267 0.265 9 0.265 0.265 10 0.268 0.267 11 0.268 0.268 12 0.265 0.269

(a) Is there a significant difference between the means of the population of measurements from which the two samples were selected? Use ???? = 0.05.

(b) Find the P-value for the test in part (a).

(c) Construct a 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers.