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AP Statistics 1.10 The Investigative Question Revisited and Data Collection- Exam Style Questions - MCQs - New Syllabus

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Question 

A manufacturing company conducts a study to compare two methods for transporting and storing methyl methacrylate to determine which method results in fewer safety concerns. Method A uses a hydroquinone-based inhibitor and Method B uses a much less common phenothiazine-based inhibitor. The researchers randomly select 20 containers of methyl methacrylate from the containers produced in a day and then randomly assign Method A to 10 of the containers and Method B to the remaining 10 containers. The researchers find that Method A has significantly fewer safety concerns than Method B.

Based on the results of the study, can the researchers state that the decrease in safety concerns is caused by the use of Method A?

(A) Yes, since the methods were randomly assigned to containers.
(B) Yes, since the containers were randomly selected from all containers.
(C) No, the methods needed to be assigned to at least 30 containers.
(D) No, since the researchers should not have both randomly selected containers and randomly assigned the methods to the containers.
(E) No, since the day for selecting the containers was not selected at random.

▶️ Answer/Explanation

The key feature of this study is that the researchers randomly assigned the two treatment methods to the containers. Random assignment allows researchers to control for lurking variables and establish a cause-and-effect relationship between the treatment and the response.

Random sampling helps with generalizing results to a larger population, while random assignment is what justifies causal conclusions. Since Method A and Method B were randomly assigned to the containers, the observed difference in safety concerns can reasonably be attributed to the treatment method.

Therefore, the researchers can conclude that the reduction in safety concerns was caused by Method A.

✅ Answer: (A)

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, or mileage. Higher mileage is considered better than lower mileage.
The researchers will contact several owners of each model of car and ask them to estimate their mileage.
Which of the following best describes this study?
(A) It is an experiment because there are four car models being compared.
(B) It is an experiment because the researchers are measuring mileage.
(C) It is an observational study because the researchers are not assigning treatments to the car owners.
(D) It is an observational study because the researchers are using exactly four groups.
▶️ Answer/Explanation

This is an observational study because the researchers are only collecting information from car owners.
The researchers are not assigning car owners to drive a specific model of car, and they are not imposing a treatment.
They are simply asking owners to estimate their mileage and then comparing the responses across models \(A\), \(B\), \(C\), and \(D\).

✅ Answer: (C)

Question

James completed his investigation using only his own Model \(D\) car. He found that 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 wants to state that the results of his hypothesis test apply to all Model \(D\) cars in the club. A statistician tells James that 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?
(A) Increase the number of days from \(70\) to \(140\), while still using only his own car.
(B) Use a random sample of Model \(D\) cars from the club, instead of using only his own car.
(C) Use autopilot on exactly \(35\) days and no autopilot on exactly \(35\) days.
(D) Record the mileage more carefully each day.
▶️ Answer/Explanation

James used only his own Model \(D\) car, so the results can reasonably apply only to conditions involving his car and his driving situation.
To generalize to all Model \(D\) cars in the club, James would need to select a random sample of Model \(D\) cars from the club and include those cars in the study.
Random sampling from the club would make the sample more representative of the population of Model \(D\) cars in the club.
Simply using more days with the same car would not solve the generalization problem, because the study would still be based on only one car.

✅ Answer: (B)

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