Two devices have been proposed to reduce the air pollution resulting from the emission of carbon monoxide (CO) from the exhaust of automobiles. To evaluate the effectiveness of the devices, 48 cars of varying age and mechanical condition were selected for the study. The amount of carbon monoxide in the exhaust (in ppm) was measured prior to installing the device on each of the cars. Because there were considerable differences in the mechanical conditions of the cars, the cars were paired based on the level of CO in their exhaust. The two devices were then ran­domly assigned to the cars within each pair of cars. Five months after installation, the amount of CO in the exhaust was again measured on each of the cars. The reductions in carbon monoxide from the initial measurements are given here.

a. Does there appear to be a difference between the two devices with respect to their ability to reduce the average amount of CO in the exhaust of the cars? Use α = .05.
b. Compute the relative efficiency of the randomized complete block design (block­ing on car) compared to a completely randomized design in which the 48 cars would have been randomly assigned to the two devices without regard to any pair­ing. Interpret the value of the relative efficiency.
c. Based on the relative efficiency computed in part (b), would you recommend pair­ing the cars in future studies?

Pair 1 234 5 67911 12 Before 2.37 3.17 3.07 2.73 349 4.35 3.65 3.97 3.21 4.46 3.81 455 After 251 265 2.60 2.40 23 2.28 094 2.21 3.29 192 3.38 2.43 Pair 13 14 1516 17 8 19 20 2 23 24 Before 451 3.03 447 3.44 352 3.0 3.66 3.81 3.13 343 3.26 2.85 After 183 263 231 185 2.92 2.26 3.1 190 2.50 3.18 3.24 2.16 5 5