Below is our AP Statistics unit 3 practice test. These questions are about the collection of data — different ways of sampling and different ways a sample may be biased. The ideas of bias, double-blind studies, control and treatment groups, experimental and observational studies, SRS (Simple Random Sampling), and stratified random sampling appear in this unit.
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Question 1 |
Which of the following types of studies are experimental, and which are observational?
I. A group of people were asked about their tea consumption, and self-reported stress levels are tracked, then compared to tea consumption.
II. A group of people are split in half, with one half being asked to meditate three times a week. Self-reported stress levels in both groups are tracked.
III. People are told to either wake up without an alarm for two weeks, or wake up at a specific time with an alarm for two weeks. Self-reported stress levels are tracked.
IV. Participants are classified as very social, moderately social, or not very social based on their number of social engagements per month. Each group is then asked to record self-reported stress levels.
All are experimental | |
I and II are experimental, and III and IV are observational | |
II and III are experimental, and I and IV are observational | |
All are observational |
Question 1 Explanation:
The correct answer is (C). In an observational study, participant behavior is recorded but there is no influence exerted over the behavior. In an experimental study, participants are in a control group and a treatment group. For options II and III participants were assigned to a specific group (meditation or alarm use) but in options I and IV participants were classified based on their current behavior. Therefore, I and IV are observational.
Question 2 |
Researchers are trying to determine whether chocolate milk can be linked to sleep difficulties. They conduct several experiments. Which of the following situations describes an appropriate conclusion for the experiment?
In a study of randomly selected high school seniors, there was a correlation between chocolate milk consumption and sleep difficulties. The conclusion drawn was that there will be a correlation between chocolate milk consumption and sleep difficulties for all adults. | |
A doctor asked all high school students in that doctors practice about their chocolate milk consumption and sleep habits. The conclusion drawn was that there is a correlation between chocolate milk consumption and sleep difficulties for all high school students. | |
Researchers surveyed high school students randomly drawn from across the country about chocolate milk consumption and sleep. The conclusion drawn was that drinking chocolate milk causes sleep difficulties. | |
Researchers surveyed high school students randomly drawn from across the country about chocolate milk consumption and sleep habits. The conclusion drawn was that there is a correlation between chocolate milk consumption and sleep difficulties for all high school students. |
Question 2 Explanation:
Answer choice (D) is the only valid conclusion that can be drawn. Answer choice (A) uses data on high school seniors generalized to a larger adult population, which is not the population from which the sample was selected. Answer choice (B) is not randomly selected and may not be appropriately representative of all high school students. Answer choice (C) attempts to determine causal relationships from an observational study, which is not possible.
Question 3 |
A principal wants to know the most popular food served in the cafeteria. Students are divided by grade, and then chosen at random from within each grade. Which sampling method was used?
Simple random sampling | |
Stratified random sampling | |
Cluster sampling | |
Systematic random sampling |
Question 3 Explanation:
The correct answer is (B). Because the groups have a shared characteristic (grade level), it is stratified random sampling, The students are divided before sampling, which eliminates choice (A). Cluster sampling would involve clusters of students with varied composition, for example choosing mixed-grade homerooms. Systematic random sampling would involve using a method of choosing students, for example, choosing every fourth person to walk into the building.
Question 4 |
A sports team wants to determine the best type of concessions to serve for the next season. The staff decides to divide ticket holders in clusters based on seat location, and then randomly choose three seating areas to survey. Which of the following is most likely to be true?
There is the potential for bias based on seat location. | |
This is guaranteed to provide a representative sample. | |
Both are true. | |
Neither are true. |
Question 4 Explanation:
The correct answer is (A). When using cluster sampling, clusters should be as representative of the general population as possible. Clustering by seat location means that one cluster may contain club seating and another may contain the least expensive seats, neither of which would be representative of the population as a whole. Dividing by seating areas is more similar to a stratified random sample, so the researchers would need to select random ticketholders from within each seating area to have a more representative sample.
Question 5 |
A school counselor wants to ask students about a potential new class. The first 100 students are asked, “Should the school add a game design course to the schedule?” Which of the following would be effective at reducing bias?
Asking the first 100 students into the school building, “Should the school add a game design course to modernize the schedule?” | |
Asking a randomly selected group of students from each grade, “Should the school add a game design course to add a new, interesting elective to the school schedule?” | |
Selecting 10 mixed-grade homeroom clusters at random and asking those students, “Should the school add a game design course to the school schedule?” | |
None of the above |
Question 5 Explanation:
The correct answer is (C). The initial situation is biased by using a convenience sample. It is highly unlikely that the first 100 students will be representative of the entire school. Answer choice (A) not only includes the selection bias, but introduces bias in the wording of the question with the addition of the word “modernize.” Answer choice (B) uses an appropriate method of choosing the sample, but uses leading words in the question by adding “new, interesting elective.” Answer choice (C) is correct — it retains the neutral question wording and uses an appropriate method of choosing the student sample.
Question 6 |
A researcher is designing an experiment to test the effectiveness of a particular educational technique for fifth-grade math. Which of these are potential confounding variables?
Education level of parents | |
Student IEPs | |
Time of year | |
All of the above |
Question 6 Explanation:
The correct answer is (D). All of these are potential confounding variables. Students whose parents have a higher educational level may adapt to educational changes more quickly or have more help at home. The balance of IEPs in a class may sway results. The time of year can impact how comfortable students are with the classroom teacher and how willing they are to adapt to a new technique.
Question 7 |
Which of the following situations illustrates an element of a well-designed experiment?
Participants are chosen at random and select their groups. | |
A group is given a treatment and data is collected before and after the treatment. | |
Participants are divided into groups based on a specific characteristic, then randomly selected from those groups to be placed into control and treatment groups. | |
None of the above. |
Question 7 Explanation:
The correct answer is (C). Answer choice (A) does not provide random assignment to groups. Answer choice (B) describes an observational study, not an experiment. Answer choice (C) illustrations random assignment to control groups, one of the elements of a well-designed experiment.
Question 8 |
What is the advantage of randomized assignment to groups in an experiment?
Makes it easier for the researcher to know who is in each group. | |
Avoids participants from being offended that they weren’t in a specific group. | |
Ensures that participants and researchers don’t know which group they’re in. | |
Helps balance the potential effects of confounding variables. |
Question 8 Explanation:
The correct answer is (D). Randomized assignment to groups helps balance the potential effects of confounding variables. Answer choice (C) describes a double-blind study. Answer choice (B) is not generally a consideration when designing an experiment. Randomized assignment doesn’t affect how easy it is for the researcher to know who is in each group.
Question 9 |
Which of the following is an advantage of a double-blind study?
It works well for all treatment types. | |
It replicates real-life conditions. | |
All studies can be done as double-blind studies. | |
It reduces bias. |
Question 9 Explanation:
The correct answer is (D). Double-blind studies do not necessarily work well for all treatment types, nor do they replicate real-life conditions, since patients are told when they are receiving treatments. Not all studies are suitable for double-blind studies. However, double-blind studies do help reduce bias because neither researcher nor participant knows who is in which group.
Question 10 |
Which of the following statements is false?
Random allocation to control and treatment groups helps researchers conclude that results are statistically significant. | |
Statistically significant results provide evidence that the treatment is effective. | |
Results can be generalized to a larger group for which the sample is considered representative. | |
All experiments with a control and treatment group can be considered well-designed experiments. |
Question 10 Explanation:
Statement (D) is false — there are other factors that are needed to be a well-designed experiment. (A), (B), and (C) are all characteristics of a well-designed experiment that can be used to establish evidence of causal relationship.
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