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AP Statistics 3.3 Random Sampling and Data Collection- FRQs - Exam Style Questions

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Question

A car maker produces four different models of cars: A, B, C, and D. A group of researchers is investigating which model of car has the longest distance traveled per gallon of gas (mileage). Higher mileage is considered better than lower mileage. The researchers will conduct a study in which they contact several owners of each model of car and ask them to estimate their mileage.
(a) Is this an observational study or an experiment? Justify your answer in context.
Model D has an autopilot feature, in which the car controls its own motion with human supervision. James owns a Model D car and will investigate whether using the autopilot feature results in higher mileage than not using the autopilot. James will drive his car on \(70\) different days to and from work, using the same route at the same time each day. James will record the mileage each day.
(b) James will use a completely randomized design to conduct his investigation. Describe an appropriate method James could use to randomly assign the two treatments, driving using the autopilot feature and driving without using the autopilot feature, to \(35\) days each.
(c) After the investigation was completed, James verified that the conditions for inference were met and conducted a hypothesis test. He discovered the mean mileage when using the autopilot feature was significantly higher than the mean mileage when not using the autopilot feature. James is a member of a Model D club with thousands of members who all drive Model D cars. He will give a presentation at a Model D club members’ meeting later this year and would like to state that the results of his hypothesis test apply to all Model D cars in his club. Another member of the club who is a statistician tells James his findings do not apply to all Model D cars in the club. What change would James need to make to his original study to be able to generalize to all Model D cars in the club?

Most-appropriate topic codes (CED):

• TOPIC 3.2: Introduction to Planning a Study
• TOPIC 3.6: Selecting an Experimental Design
• TOPIC 3.3: Random Sampling and Data Collection
▶️ Answer/Explanation
Detailed solution

(a)
This is an observational study. The researchers are collecting data by asking car owners to estimate their mileage without imposing any treatments. The owners are not randomly assigned a car model to drive.

(b)
James can number the days of the experiment from \(1\) to \(70\). Then, using a random number generator, he can generate \(35\) unique integers from \(1\) to \(70\).The days corresponding to these \(35\) numbers will be assigned to the “drive with autopilot” treatment. The remaining \(35\) days will be assigned to the “drive without autopilot” treatment.

(c)
James’s experiment only used his own car, so the results can only be generalized to his specific car and driving conditions. To generalize the findings to all Model D cars in his club, he would need to conduct a new study. In the new study, he must randomly select a sample of Model D cars  from the club’s members. He would then need to carry out a similar experiment using the randomly selected cars.

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