Question 17 • Probability and Statistics with Applications Honors Sem-1-FL-1210300 (2024-2025)
A tire company wants to determine if tires made with a new type of tread will last longer than tires made with the original type of tread. The company has access to 24 different vehicles. Each vehicle will receive four tires with the new tread and four with the original tread. The position, front or back, will be randomly determined for a pair of each type of tread. For example, a vehicle will have the new type of tread on the front tires and the original tread on the back tires. After six months, the pairs of unused tires will be used with the position switched on the car. The vehicles will be driven for six more months. At the end of one year, the depths of the remaining tread will be measured for each tire and the average differences between the new and original tread types will be determined. The average differences will then be used to determine if the new tread does last longer.
Answer
A
Yes, the company used 24 different vehicles.
B
Yes, both types of tread were randomly assigned to each vehicle.
C
No, the vehicles were not put into groups of two.
D
No, the tires with the different types of tread were not randomly assigned to each vehicle.
Explanation
This is a matched-pairs experiment because each vehicle receives both tread types, so the comparison can account for differences between vehicles. The front-or-back position for each tread type is randomly determined, and the positions are switched after six months to reduce the effect of tire location. Thus, both tread types are randomly assigned within each vehicle; choice B is correct.
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