The two tires on a bicycle experience wear much in the same way car tires do; repeated contact with the road or sidewalk will wear down the raised rubber, giving the tire less traction. A major tire manufacturer has developed a new bicycle tire design they hope will reduce wear. After running several rounds of testing in laboratory conditions, they want to test the tires in real-life biking conditions. They find 20 volunteers who bike on a daily basis. The volunteers are each given a new bike of the same model for the duration of the experiment. The volunteers are to bike as they normally would for a month, then return the bike to have the wear of the tires measured, determined by millimeters of tire depth remaining. The manufacturer knows these results must be compared to their standard model tire, so they will use the standard model in the experiment as a control group.

a) The manufacturer determines a matched pair design would be most appropriate to compare the wear of the new tire design to the standard design. Describe how to implement a matched pair design for this experiment.

b) Describe the primary advantage of using a matched pair design in the context of this experiment.

c) At the conclusion of the experiment, the manufacturer finds that the new tire design has experienced statistically significantly less wear than the standard tire design. Can the manufacturer infer that the new tire will cause significantly less tire wear for all bikers? Explain.

Unit 3 Practice Free Response Question The two tires on a bicycle experience wear much in the same way cartires do; repeated contact with the road or sidewalk will wear down the raised rubber, giving the tire less traction. A major tire manufacturer has developed a new bicycle tire design they hope will reduce wear. After running several rounds of testing in laboratory conditions, they want to test the tires in real-life biking conditions. They find 20 volunteers who bike on a daily basis. The volunteers are each given a new bike ofthe same model forthe duration ofthe experiment. The volunteers are to bike as they normally would for a month, then return the bike to have the wear of the tires measured, determined by millimeters oftire depth remaining. The manufacturer knows these results must be compared to their standard model tire, so they will use the standard model in the experiment as a control group. a) The manufacturer determines a matched pair design would be most appropriate to compare the wear of the new tire design to the standard design. Describe how to implement a matched pair design for this experiment. b) Describe the primary advantage of using a matched pair design in the context of this experiment. c) At the conclusion of the experiment, the manufacturer finds that the new tire design has experienced statistically significantly less wear than the standard tire design. Can the manufacturer infer that the new tire will cause significantly less tire wear for all bikers? Explain. -|- STATS MEDIC