📊AP Statistics Review
AP Stats Unit 3 FRQ Practice Prompt Answers & Feedback
AP Stats Unit 3 FRQ Practice Prompt Answers & Feedback
FRQ practice is one of the most important ways to prepare for the AP Stats exam! Practice writing a response to this prompt focused on unit 3 (experiments and observational studies). Then review these student writing samples with corresponding feedback from Fiveable teacher Jerry Kosoff!
On the AP Statistics Exam, Section II has 6 free-response questions: 5 Part A questions in 65 minutes and 1 investigative task in 25 minutes. According to the current exam description, the five Part A questions include one question primarily focused on collecting data, one on exploring data, one on probability and sampling distributions, one on inference, and one that focuses on two or more skill categories. The investigative task in Part B assesses multiple skill categories.
A collecting-data question like this typically aligns with one of the Part A free-response questions focused on study design, experiments, sampling, or bias.
A Unit 3 collecting-data FRQ primarily assesses selecting statistical methods, especially identifying key information and describing an appropriate study design. It also commonly assesses statistical argumentation, because students must justify why the study is an experiment, explain what conclusions are and are not warranted, and interpret design features like blinding in context.
On the AP Statistics exam, a study is an experiment because researchers deliberately impose treatments on subjects; in this prompt, volunteers were assigned to receive either the medication or the placebo. The strongest AP justification is to mention the imposed treatments and the random assignment.
FRQ Unit 3 Exam Practice Prompt
Exposure therapy is a technique used to help individuals overcome their fears, by slowly introducing them to the things of which they are afraid. This typically requires many visits to a therapist; often 8 or more. Researchers are wondering if a new medication, used in combination with fewer exposure therapy sessions, can aid individuals in overcoming their fears. To study the new medication’s effect, 50 volunteers with a fear of spiders (arachnophobia) were recruited for a study along with a set of therapists trained in exposure therapy. The volunteers were all told that they would be participating in five therapy sessions, and before each session were also instructed to take a pill given to them by the researchers. The volunteers were randomly assigned one of two pills to take throughout the study: 25 received a pill containing the new medication, while 25 received an identical-looking placebo pill. Two months after their five therapy sessions were conducted, the volunteers were evaluated to determine the amount of improvement in their fear.
- a. Was this study an experiment or observational study? Justify your decision.
- b. After the study, it was determined that the group that received the new medication showed levels of improvement that were statistically significantly higher than the group that received the placebo. Based on this result and the design of the study, would the researchers be justified in claiming that the new medication could be useful in helping individuals similar to those in the study overcome any of their fears?
- c. A newspaper article that summarized the results of the study mentioned that it was done in a “double-blind fashion.” Explain what that means in the context of this study.
FRQ Writing Samples and Feedback
FRQ Practice Submission 1
(a) This is an observational study as the individuals were volunteers and not randomly selected. Since they were volunteers, the results may not generalize to a broader population. This makes is seem like that at the end of the therapy sessions, the pills worked in regards to having less of a fear of spiders. There was also no replication done in this experiment.
(b) No, because this is not a well designed experiment.
(c) A double-blind fashion in this case means that the individuals receiving the medicine were not told if it was an actual pill or placebo pill and the therapists didn’t know which patients had the actual pill or placebo pill. This ensures that during the therapy session, the therapists and individuals treat one another the same as they both don’t know what’s happening,
Teacher FRQ Feedback
In part (a), it appears that you’ve mixed up the purpose of random selection (which is not present in the scenario, as you mention) and random assignment (which is present in the scenario). Random ASSIGNMENT (of treatments) is the key distinguishing factor between an experiment and observational study; therefore this scenario is in fact an experiment. Because the prompt states the subjects were volunteers with a fear of spiders, all subjects in the study had arachnophobia. The real issue is not whether they had the condition, but that they were volunteers rather than a random sample, so the results may not generalize to a broader population. In part (b), the better explanation is this: Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. Because your reasoning in part (b) is consistent with your response in part (a), your response would still likely show some correct thinking on part (b), though part (a) would not earn credit. Your response in part ( c ) is spot-on, and includes a benefit of blinding. This response includes the key statistical ideas AP readers look for: identifying who is blinded in context and noting how blinding helps reduce bias.
FRQ Practice Submission 2
a) This was an experiment because random assignment was used to put participants to either get the new medication or a placebo pill to compare the results of improvement in arachnophobia in the participants.
b) Due to the experiment not using random selection, we cannot determine causation between the new medication and improvements in arachnophobia. Only experiments with randomization can have causality between variables.
c) A double blind technique in this procedure means that the participants are unaware if they are getting the new medication or taking the placebo pill. Additionally, the therapists are also not aware what pills they participants are getting which reduces experimenter bias. This ensures that both researchers and participants do not form any conclusions or start acting in a different way due to knowing which treatment they have or their participants have.
Teacher FRQ Feedback
Your response is very solid!
In part (a), you make it clear which treatments were assigned (“new medication or a placebo pill”) which correctly answers the question and includes context of the problem. This response includes the key statistical ideas AP readers look for: imposed treatments and random assignment.
In part (b), your answer of “no” is correct but your explanation for why is not all the way there. You mention that there is not random selection, but then state that this implies we cannot determine causation. That is an incorrect statement: we can determine causation due to the random assignment of treatments. Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. Therefore, this response may earn some credit for the correct “no,” but it needs a more accurate justification.
In part ( c ), you give a strong description of the meaning of “double-blind” and include appropriate context from the scenario. This response includes the key statistical ideas AP readers look for: the subjects did not know their treatment, and the therapists and/or evaluators interacting with them also did not know.
FRQ Practice Submission 3
a) This study was an experiment. This is because the experimental units, volunteers, were randomly assigned either the placebo pill or the pill with the new medication. Because treatments are imposed on individuals and their fear of spiders (response variable) is being measured, this is an experiment.
b) Because the volunteers were not randomly selected from a broader population, the researchers may conclude a cause-and-effect relationship for the volunteers who participated, but they cannot generalize the results to a broader population of people with fears. Thus, they would not be justified in claiming that the new medication could be useful in helping individuals similar to those in the study overcome any of their fears.
c) A “Double-blind” fashion in the context of this study means that the volunteers did not know whether they received the medication or the placebo, and the therapists and/or evaluators who interacted with the volunteers or measured improvement also did not know which treatment each volunteer received.
Teacher FRQ Feedback
In part (a), you clearly justify why this is an experiment, including a description of assigned treatments. This response includes the key statistical ideas AP readers look for: imposed treatments and random assignment.
In part (b), the key idea should include both limits clearly: Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. This response includes the key statistical ideas AP readers look for: causation from random assignment, but limited generalization because of volunteers and the narrow scope of fear studied.
Finally, in part ( c ), you give a clear description of “double-blind” in the context of this study. This response includes the key statistical ideas AP readers look for. Nicely done.
FRQ Practice Submission 4
a. This study was an experiment. There was a treatment (the pill) given to some of the volunteers, and because there was treatment, it is an experiment and not just an observational study.
b. Yes, since it was an experiment, the researchers can assign causation to individuals similar to ones in the study.
c. “Double-blind fashion” means that neither the individuals in the study or the therapists knew if the individual was taking the placebo drug or the new medication. Experiments use double blinding so that the treatment does not change. It ensures that the results are solely determined based on the medication.
Teacher FRQ Feedback
In part (a), you are right that this is an experiment, but the strongest AP justification is that treatments were deliberately imposed and randomly assigned. Be careful with saying “because there was treatment” - that makes it sound like merely having a treatment automatically makes something an experiment. A more precise answer would mention that the volunteers were assigned to one of two treatments, the medication or the placebo.
In part (b), you will not earn credit. Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear.
In part ( c ), you give a correct description of what “double-blind” means in the context of this study, though your second sentence is a bit vague: “the treatment does not change.” You may be referring to the idea that we blind participants to their treatment so that their behavior within the experiment does not change; once they are assigned their treatments, the treatment itself would not change. You would likely earn credit for your response, but be careful with the precision of your descriptions.
FRQ Practice Submission 5
a.) This study was an experiment because the volunteers were randomly assigned to either pill (new medication or placebo). There are treatments being assigned to the volunteers to see if their fear of the spiders improves.
b.) Because the volunteers were not randomly selected from a broader population, the researchers may conclude a cause-and-effect relationship for the volunteers who participated, but they cannot generalize the results to a broader population of people with fears. Therefore, they cannot claim that the new medication could be useful in helping individuals similar to those in the study overcome any fears.
c.) If the experiment was done in a “double-blind fashion,” the volunteers who were being evaluated to determine the amount of improvement in their fear would not know whether they received the new pill or the placebo pill. In addition, the evaluators would not know which treatment each volunteer received. This would limit any bias in which the individuals would lean a certain way due to them knowing that they were given the new medication/placebo.
Teacher FRQ Feedback
I have less feedback for this response… but that’s because you did very well! In part (a), you give the correct answer, with a correct reason in context (assignment of the specific treatments). In part (b), the key idea should include both limits clearly: Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. In part ( c ) you clearly explain what blinding is and its purpose in the context of this study. Well done!
FRQ Practice Submission 6
A. This study is an experiment because the 50 volunteers were randomly assigned to one of two treatments, the new medication or a placebo, and the researchers measured the response after imposing those treatments.
B. No, the researchers would not be justified in claiming that the new medication could be useful in helping individuals similar to those in the study because this experiment is not well designed, there is selection bias. In the experiment, it explicitly stated that the experimental units were volunteers meaning that those people chose to be in the sample. Therefore, it would be incorrect to generalize the results of this study to others that have the same fears.
C. In the context of this study, double-blind fashion indicates that neither the 50 volunteers nor the sets of therapists knew who received the new medication or the placebo.
Teacher FRQ Feedback
Your part (a) is already correct and sufficiently precise for AP Statistics: random assignment to the medication or placebo treatment makes this an experiment.
In part (b), your “no” is on the right track because the subjects were volunteers rather than a random sample. To make it fully complete, also note that the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear.
In part ( c ) , you give a concise and correct description of being “double-blind,” in context. Well done!
FRQ Practice Submission 7
a) This study was an experiment because a specific treatment was assigned to the participants in the therapy session. The treatment was the pill containing the new medication or the placebo assigned to patients to compare the results of improvement in arachnophobia. Additionally, the treatments were randomly assigned to patients.
b) No. Because the volunteers were not randomly selected from a broader population, the researchers may conclude a cause-and-effect relationship for the volunteers who participated, but they cannot generalize the results to a broader population of people with fears.
c) The researchers assigning the treatment - pills containing the medication vs the placebo, did not themselves know which type of pill they were assigning the volunteers in this experiments. Additionally, the volunteers also didn’t know which type of pill they were receiving.
Teacher FRQ Feedback
Your responses are thorough and in-context for all three parts. In part (a), good job naming the treatments that were assigned as a part of your justification. In part (b), the key idea should include both limits clearly: Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. In part ( c ) you correctly define double-blinding, though it would be even more precise to name the volunteers and the therapists and/or evaluators who interacted with them or measured improvement. Nicely done!
FRQ Practice Submission 8
A) This study is an experiment as the researchers are imposing a treatment on the groups in the therapy session. The volunteers were randomly assigned either the treatment of the pill containing medication or the placebo pill before their therapy sessions to compare the amounts of improvement in their fear of spiders.
B) No. Because the volunteers were not randomly selected from a broader population, the researchers may conclude a cause-and-effect relationship for the volunteers who participated, but they cannot generalize the results to a broader population of people with fears.
C) Double-blind means that the volunteers did not know whether they received the medication or the placebo, and the therapists and/or evaluators who interacted with the volunteers or measured improvement also did not know which treatment each volunteer received.
Teacher FRQ Feedback
Very strong on all three parts. In part (b), the best explanation is this: Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. Nice work.
FRQ Practice Submission 9
a) This is an experimental study because volunteers are given either a placebo or the new medication as treatment.
b) No, because this study was done specifically based on volunteers with fear of spiders.
c) Double-blind tells us that neither the volunteers taking the pill or the therapists working with the volunteers knew whether the volunteer was taking the new medication or a placebo.
Teacher FRQ Feedback
Nice answers! Part (b) gives a good reason but may need to be explained a little more (“volunteers with fear of spiders, meaning that those people would not be representative of the larger population described”) or something like that. You could also explicitly mention that the study only involved arachnophobia, so it does not justify a claim about overcoming any fear. (a) and ( c ) gives an appropriate level of context for your answers.
FRQ Practice Submission 10
a) This study is an experiment because it involves the random assignment of treatment: one group was given the new medication and the other was given a placebo.
b)The researchers would not be justified in claiming that the new medication could be useful in helping individuals similar to those in the study overcome any of their fears. The study was conducted using volunteers who suffered from arachnophobia and the medication does not appear to be tested against any other fears, therefore the results from this study could not be used to support the medications effectiveness in helping overcome any fears. This study also lacks random selection as it was conducted using volunteers who were recruited to participate, making the sample not a representative sample.
c) In this context, “double blind” means that the participants were unaware of the type of pill they were given (medication vs placebo) and the therapists and/or evaluators who interacted with the volunteers or measured improvement also did not know which treatment each volunteer received. This avoids any experimenter bias and makes sure that the participants do not change their behavior and experimenters do not make false conclusions as a result of knowing the type of treatment the participant receives.
Teacher FRQ Feedback
Good work on all three parts - clear, descriptive responses in context of the scenario. This response includes the key statistical ideas AP readers look for: random assignment for causation, the lack of random selection for broad generalization, and the fact that the study only involved arachnophobia rather than any fear.
FRQ Practice Submission 11
a. The study was an experiment because the pills that the volunteers were given (medicated or placebo) was a treatment imposed.
b. No because the researchers would only be able to draw conclusions based on the sample and not apply it to a population. In order to do that they would need to carry out an inference test to conclude whether the researchers could claim that the new medication showed statistically significant results.
c. A double blind experiment is used to eliminate any potential bias to the experiment by ensuring that neither the volunteers nor the researchers knew which pill each volunteer was receiving. Since neither party knows which pill each volunteer is receiving, it eliminates a potential source of bias of knowing whether the pill was real or placebo which could have affected results.
Teacher FRQ Feedback
Solid work!
In part (a), you are right that treatments were imposed, but the strongest AP justification would be to mention both imposed treatments in context and, ideally, the random assignment to medication or placebo.
In part (b), you give the correct answer (“no”), but don’t give the correct reason for why we cannot apply the results to the population. In our case, the sample is not representative of the population because the subjects were volunteers and they all had one specific fear. Because the subjects were volunteers rather than a random sample, the study’s results should not be generalized broadly to a larger population. Random assignment does support a cause-and-effect conclusion for the volunteers in this study, but lack of random selection limits external validity.
In part ( c ), your explanation would be more precise if you named the people who were blinded in this study: the volunteers and the therapists and/or evaluators who interacted with them or measured improvement. Well done overall.
FRQ Practice Submission 12
a) this was an experiment because there were treatments randomly assigned to the patients ( placebo and the new medication) to compare the results of improvement of arachnophobia in patients.
b) no because the volunteers were not randomly selected from a broader population, so the researchers may conclude a cause-and-effect relationship for the volunteers who participated, but they cannot generalize the results to a broader population of people with fears.
c) a double blind method means that the volunteers did not know whether they received the medication or the placebo, and the therapists and/or evaluators who interacted with the volunteers or measured improvement also did not know which treatment each volunteer received.
Teacher FRQ Feedback
Nice job! Your answers are short, but contain all appropriate information that would show readers that you understand. In part (b), the fully complete reasoning is this: Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. Your answer is strong and likely earns credit, but the most complete AP-style justification would also note that the study only involved people with arachnophobia, so the results do not justify a claim about overcoming any type of fear.
FRQ Practice Submission 13
a) This was an experiment because the experimental units (volunteers) were deliberately acted upon (given a placebo or the new medication).
b) Yes, because this experiment’s design follows the basic principles of experimenting. First, the experiment has multiple treatments (placebo and actual medication) with one being a control allowing for accurate comparison. The experiment uses random assignment to assign the volunteers to the placebo or the new medication which reduces any sort of bias. The experiments keeps as many variables the same as possible by selecting volunteers with the same phobia (arachnophobia). Finally, the experiment uses replication by having a size of 50 volunteers which will account for most variability,
c) A double-blind is when the subjects in an experiment and those collecting data/interacting with the subject do not know which subject got which treatment. In this context, a double-blind would mean that the subjects and the therapists do not know which subject got the placebo pill or the new medication pill.
Teacher FRQ Feedback
In part (a), you give an appropriate reason for “experiment” (naming treatments in context). Nice job.
In part (b), be careful. A well-designed experiment allows us to make explicit cause-and-effect conclusions based on treatments, but does not necessarily allow us to generalize beyond those in the study. Random assignment allows the researchers to conclude that, for the volunteers in this study, the medication caused greater improvement than the placebo. However, because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear.
Part ( c ) is well done.
FRQ Practice Submission 14
a. This study was an experiment. There are two groups, each with 25 individuals. The volunteers were randomly assigned one of two treatments; either a new medication, or a placebo ( the control group). Since this study has a control group and is specifically using a treatment group to affect the results.
b. Although the experiment is controlled, randomized, and shows comparison between two treatments (placebo and actual medication), the experiment must have many more people randomly selected from the population so that random selection doesn’t impact the result of the experiment significantly or replicate the design on multiple units to reduce variation. Even if the design wasn’t flawed, it cannot be generalized to all fears, but only fears that were tested in this experiment (arachnophobia)
c. In this double-blind experiment, the therapists as well as the volunteers with arachnophobia do not know whether the participants are taking a pill filled with a new medication that is supposed to aid in overcoming their fear, or a identical- looking placebo pill.
Teacher FRQ Feedback
In parts (a) and (b), you give the correct answers but ended up saying a little too much - potentially jeopardizing full credit. For part (a), you correctly mention random assignment of medicine/placebo as the reason for this being an experiment, but then go on to say that “this study has a control group.” That is true, but just having a control group does not guarantee that any particular scenario is an experiment; your answer makes it sound like it does. That could be enough to deduct. Do not say the 25 individuals in each group were randomly selected. The study used volunteers, then randomly assigned them to medication or placebo. Random assignment makes this an experiment; random selection did not occur.
Then in part (b), you correctly identify that we can’t generalize from people with arachnophobia to people with any fear, but also comment on the sample size. Small samples - when randomly selected - can be representative of populations from which they come, so that by itself isn’t a good reason to say no. The better explanation is that random assignment allows a cause-and-effect conclusion for the volunteers in this study, but because the subjects were volunteers rather than a random sample, the results should not be generalized broadly. In addition, the study only involved people with arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. In part ( c ), you give a correct explanation of double-blind. No issues there. :)
FRQ Practice Submission 15
a) Since there was a treatment imposed being that the volunteers or test subjects had to take the pills and go to therapy, this was an experiment. After this experiment you are able to compare the effects of the pill in order to assess weather it helps the individuals overcome their fears or not.
b)The volunteers were randomly assigned to either placebo or medication pills, implying causation, and the amount of them being 50 is surely less than 10 percent of the population with fears numbering in the thousands if not more and the new medication showed levels of statistically significant improvements. However, because the test subjects were volunteers and not obtained randomly, the results should not be generalized to other people, even if they seem similar.
c) Double blind means that both the test subjects getting the treatment and the therapists and/or evaluators who interacted with the volunteers or measured improvement do not know which treatment is for which test subject. In context, the volunteers would be told they are both getting pills but not know if they were getting the placebo or medication. Also, the people giving them the pills would not know who they were giving which pills to(the pills would probably look the same and be in one box and the “giver of pill people” would just grab one set and hand it to the volunteer). The only people who would know who got what pill type would be the analysts who wanted to see if the data was statistically significant and be unable to affect the results of the experiment as they would receive this information post-experiment.
Teacher FRQ Feedback
Strong responses overall! In part (a), be a little more precise: on AP Statistics, the strongest justification is that researchers deliberately imposed treatments, and here the volunteers were randomly assigned to one of two treatments, medication or placebo. Part (b) should say that random assignment allows a cause-and-effect conclusion for the study participants, but because the subjects were volunteers with a specific fear and were not randomly selected from a broader population, the results should not be generalized to other people, even if they seem similar. Also, for full precision in this prompt, the study only involved arachnophobia, so the researchers are not justified in claiming the medication would help people overcome any type of fear. I also appreciate the phrase “giver of pill people” and may or may not borrow it in the future, lol