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AP Statistics 3.7 Inference and Experiments- FRQs - Exam Style Questions

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Question

A developer wants to know whether adding fibers to concrete used in paving driveways will reduce the severity of cracking, because any driveway with severe cracks will have to be repaired by the developer. The developer conducts a completely randomized experiment with \(60\) new homes that need driveways. Thirty of the driveways will be randomly assigned to receive concrete that contains fibers, and the other \(30\) driveways will receive concrete that does not contain fibers. After one year, the developer will record the severity of cracks in each driveway on a scale of \(0\) to \(10\), with \(0\) representing not cracked at all and \(10\) representing severely cracked.
(a) Based on the information provided about the developer’s experiment, identify each of the following.
• Experimental units
• Treatments
• Response variable
(b) Describe an appropriate method the developer could use to randomly assign concrete that contains fibers and concrete that does not contain fibers to the \(60\) driveways.
Suppose the developer finds that there is a statistically significant reduction in the mean severity of cracks in driveways using the concrete that contains fibers compared to the driveways using concrete that does not contain fibers.
(c) In terms of the developer’s conclusion, what is the benefit of randomly assigning the driveways to either the concrete that contains fibers or the concrete that does not contain fibers?

Most-appropriate topic codes (CED):

• TOPIC 3.5: Introduction to Experimental Design
• TOPIC 3.6: Selecting an Experimental Design
• TOPIC 3.7: Inference and Experiments
▶️ Answer/Explanation
Detailed solution

(a)
• Experimental units: The \(60\) individual driveways.
• Treatments: Concrete with fibers and concrete without fibers.
• Response variable: The severity of cracks recorded after one year on a scale of \(0\) to \(10\).

(b)
First, number each of the \(60\) driveways from \(1\) to \(60\). Then, use a random number generator to select \(30\) unique integers from \(1\) to \(60\). The driveways corresponding to these \(30\) numbers will be assigned to receive concrete with fibers. The remaining \(30\) driveways will receive concrete without fibers.

(c)
The benefit of randomly assigning the treatments is that it allows the developer to draw a cause-and-effect conclusion. Since the driveways were randomly assigned, it helps to ensure that the two treatment groups are roughly balanced on all other potential confounding variables at the beginning of the experiment. Therefore, if there is a statistically significant difference in the severity of cracks, the developer can conclude that it was the type of concrete (the treatment) that caused the difference.

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