Some people believe that higher-octane fuels result in better gas mileage for their car. To test this claim, a researcher randomly selected 11 individuals to participate in the study. Each participant received 10 gallons of gas and drove his car on a closed course. The number of miles driven until the car ran out of gas was recorded . A coin flip was used to determine whether the car was filled up with 87-octane or 92-octane first, and the driver did not know which fuel was in the tank. 87_octane 235 257 244 214 114 286 314 230 192 203 548
92_octane 236 237 230 224 119 296 350 240 185 209 562

N Mean StDev SE Mean
92 Octane 1111 262.545262.545 115.038115.038 34.68534.685
87 Octane 1111 257.909257.909 109.354109.354 32.97132.971
Difference 1111 4.6364.636 15.04215.042 4.5354.535

Required:
a. Why is it important that the matching be done by driver andâcar?
b. Why is it important to conduct the study on a closedâtrack?