AnswersNC-Math 4 CRExperimental DesignsQuestion 7
7
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Experimental Designs

Question 7 • NC-Math 4 CR

A tire company wants to determine if tires made with a new type of tread will last longer than the tires made with the original type of tread. The company has access to 24 different vehicles. The vehicles will be driven for one year and the depth of the remaining tread will be measured. The average depth for the new type of tread will be compared to the average depth of the original type of tread.

Answer
A
There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. For each type, three vehicles will be randomly selected to receive tires with the new tread and the other three vehicles will receive tires with the original tread.
B
Each vehicle is numbered 1–24, and these numbers are put into a random number generator. The first 12 unique numbers represent the vehicles that will receive the tires with the new tread. The remaining 12 vehicles will receive the tires with the original tread.
C
The vehicles will be put in groups of two based on the size of the vehicle, with the largest two put together, the next largest two, etc. For each of the 12 pairs, the largest vehicle will get tires with the original type of tread and the other vehicle in the pair will get the new type of tread.
D
There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. Each vehicle type is numbered 1–4, and these numbers are entered into a random number generator. The first two unique numbers selected will represent the group of vehicles that will receive tires with the new type of tread. The remaining 2 groups will receive tires with the original tread.

Explanation

Vehicle type can affect how quickly tires wear, so the comparison should account for vehicle type. Choice A randomly assigns three vehicles of each type to each tread treatment, balancing sedans, SUVs, minivans, and trucks across the two groups. Choice B assigns vehicles randomly but could leave one group with more of a particular vehicle type, while choices C and D do not properly randomize individual vehicles between treatments within each type.

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