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AP Statistics 3.2 Introduction to Planning a Study - MCQs - Exam Style Questions

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Question

The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city’s effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department?
(A) A census
(B) A sample survey
(C) An experiment with a completely randomized design
(D) An experiment with a randomized block design
(E) An experiment with a matched-pairs design
▶️ Answer/Explanation
Detailed solution

1. Analyze the Method:
– The department is collecting data from a subset of the population (a “random sample of residents”), not the entire population.
– They are asking questions to gather information about opinions without imposing any treatment.

2. Evaluate the Options:
– A census (A) would involve asking *all* residents.
– An experiment (C, D, E) would involve applying a treatment and observing the effect.
– A sample survey (B) involves selecting a sample from a population and asking them questions.

The method described is a classic example of a sample survey.
✅ Answer: (B)

Question

As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis.
What are the population and the sample of the study?
(A) The population is the 770 students who were selected, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis.
(B) The population is the 770 students who were selected, and the sample is whether each student in the survey uses the exercise facility on a regular basis.
(C) The population is the 34,000 students who attend the university, and the sample is whether each student in the survey is male or female.
(D) The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected.
(E) The population is the 34,000 students who attend the university, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis.
▶️ Answer/Explanation
Detailed solution

1. Define Population:
The population is the entire group about which we want to draw conclusions. The administrators want to estimate facility usage for all students at the university. Therefore, the population is the 34,000 students who attend the university.

2. Define Sample:
The sample is the subset of the population from which data are actually collected. The study selected a group of 370 male and 400 female students, for a total of 770 students. This group is the sample.

3. Distinguish Sample from a Statistic:
The 493 students who reported using the facilities are a result or a statistic obtained from the sample, not the sample itself. The sample is the entire group that was surveyed.

✅ Answer: (D)

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