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# AP Stats Unit 3 FRQ Practice Prompt Answers & Feedback

Jerry Kosoff

### AP Statisticsย ๐

265ย resources
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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!

## 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 medicationโ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.
• 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 โdouble-blind fashion.โ 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, some may no have had the fear of spiders. 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 didnโ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 donโt know whatโs happening,

Teacher FRQ Feedback

In part (a), it appears that youโve mixed up the purpose of randomย selectionย (which is not present in the scenario, as you mention) and randomย assignmentย (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. However, since there is not randomย selection, we would not be able to generalize the results of the experiment to other fear types, so we would still say โnoโ in part (b), but for a different reason. Because your reasoning in part (b) is consistent with your response in part (a), you would still likely be able to earn at least partial credit in part (b), though part (a) would be marked incorrect. Your response in part ( c ) is spot-on, and includes a benefit of blinding. It would earn โEโ

### 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

In part (a), you make it clear which treatments were assigned (โnew medication or a placebo pillโ) which correctly answers the question and includes context of the problem. This would earn โEโ (full credit)
In part (b), your answer of โnoโ 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. In this case, the fact that weโre lacking randomย selectionย means that we cannotย generalizeย the results of the study to a larger population beyond those who were involved in the experiment. Additionally, the question mentions โany fears,โ but this experiment specifically dealt with volunteers with a specific fear (arachnophobia). So the volunteers would not be a representative sample (which is made โworseโ by the lack of random selection). Therefore, your response will either earn โPโ (partial) or โIโ (incorrect), depending on the rubric for that year (since this is a made-up question I canโt say for sure, some rubrics are more โgenerousโ than others)
In part ( c ), you give a strong description of the meaning of โdouble-blindโ and include appropriate context from the scenario. This would earn โEโ (full credit).

### 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 experiment used volunteers who took the new medication and the placebo pill, the researchers can only generalize the statistically significant levels of improvement in level of fear to the volunteers in the study. 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 โDouble-blindโ fashion in the context of this study means that neither the volunteers nor the researchers (who interacted with the volunteers and measured their fear of spiders) knew whether the volunteers were given the pill containing the new medication or the identical-looking placebo pill.

Teacher FRQ Feedback

In part (a), you clearly justify why this is an experiment, including a description of assigned treatments. โEโ for this part.
In part (b), you explain why we cannot generalize beyond this group ofย volunteers, showing a clear understanding of the difference between randomย selectionย and randomย assignment. โEโ here as well.
Finally, in part ( c ), you give a clear description of โdouble-blindโ in the context of this study. "E"s all around! 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. โDouble-blind fashionโ 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 clearly describe why this is an experiment (โa treatment (the pill) was givenโฆโ), including context from the scenario. Be careful with saying โbecause there was treatmentโ - you make it sound like the pill was the only treatment assigned, when there were in fact two treatments assigned - the pill and the placebo. On some rubrics that would be enough to knock you down from โEโ (full credit) to โPโ (partial credit)
In part (b), you will not earn credit. Randomย assignmentย was used in this experiment, but since the people participating wereย volunteers with one specific fear, we cannot assume that they are representative of the larger population of people with any fear. Randomย selectionย of individuals could have allowed this generalization to happen.
In part ( c ), you give a correct description of what โdouble-blindโ means in the context of this study, though your second sentence is a bit vague: โthe treatment does not change.โ You may be referring to the idea that we blind participants to their treatment so that theirย behaviorย 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.) The experiment had volunteers who either took the new medication or took the placebo pill in which they cannot claim that the new medication could be useful in helping individuals similar to those in the study who overcame any fears. They can only generalize within the group they experimented with that there was an improvement in the level of fear.
c.) If the experiment was done in a โdouble-blind fashion,โ 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 that volunteers would be given. 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 responseโฆ but thatโ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), you explain that โvolunteersโ will limit our scope of inference, and in part ( c ) you clearly explain what blinding is and itโs purpose in the context of this study. Well done!

### FRQ Practice Submission 6

A. This study is an experiment because the investigators applied a treatment (the new medication) to the experimental units (the 50 volunteers) and then proceeded to observe the effects the new medication on the volunteers.
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

In part (a), you correctly choose โexperimentโ and clearly connect this to the assignment of the treatment. However, you only mention one treatment being assigned, when there was also a placebo assigned - which also counts as a treatment. Be sure to say something like โsince the volunteers were assigned either the medication or the placeboโ.
In part (b), you explain that volunteers cannot be used to generalize to a larger population, even mentioning that there may have been selection bias. Good work.
In part ( c ) , you give a concise and correct description of being โdouble-blind,โ 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, the researchers cannot be justified in claiming that the new medication could be useful in helping individuals similar to those in the study. The researchers implemented the treatment of pills containing the medication vs. placebos to volunteers, so the researchers can only generalize the statistically significant results to participants in this experiments, not individuals similar to the participants in this experiment.
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 didnโ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), you correctly connect the scenario to volunteers; in part ( c ) you correctly define double-blinding. 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, researchers are not 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 problem explicitly states that the experimental units given the medication or the placebo were volunteers. Therefore, researchers can generalize these statistically significant results to the participants in this experiment, not those individuals similar to those in the study.
C) Neither the researchers nor the experimental units know what treatment was given to the participants. In other words, the researchers didnโt know which pill (either medication or placebo) was given to each participant, and each participant was not aware of which treatment they were given as well.

Teacher FRQ Feedback

Perfect on all three parts!

### 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 aย littleย more (โvolunteers with fear of spiders, meaning that those people would not be representative of the larger population describedโ) or something like that. (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, โdouble blindโ means that the participants were unaware of the type of pill they were given (medication vs placebo) and the researchers administering the medication were not aware of which pill the subjects 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. Should earn full credit.

### 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 give a correct reason for โexperimentโ using in-context descriptions of the treatments.
In part (b), you give the correct answer (โnoโ), but donโ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 (volunteers with one specific fear cannot represent the population of people with all fears). Weย couldย do an inference procedure hereโฆ but because our sample is not representative, it would provide meaningless results.
In part ( c ), you give a good description of the meaning of โdouble-blind,โ including a reason for doing so. Well done!

### 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 experiment used volunteers who took the new medication and the placebo the researcher can only generalize the statistically significant findings and result to the volunteers in the study.
c) a double blind method means that neither the volunteers nor the researchers (measurers) do not know which medication they took.

Teacher FRQ Feedback

Nice job! Your answers are short, but contain all appropriate information that would show readers that you understand. You should earn full credit.

### 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 experimentโ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 โexperimentโ (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 doesย notย necessarily allow us to generalize beyond those in the studyโฆ we can only do that if the experimental units are representative of a larger population. In this scenario, preciselyย becauseย the volunteers explicitly had one specific fear, we cannot generalize the results to people withย anyย fear.
Part ( c ) is well done.

### FRQ Practice Submission 14

a. This study was an experiment. There are two groups, each with 25 randomly selected 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 doesnโt impact the result of the experiment significantly or replicate the design on multiple units to reduce variation. Even if the design wasnโ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 โthis study has a control group.โ 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. Then in part (b), you correctly identify that we canโt generalize from people with arachnophobia to people with any fear, but also comment on the sample size. Small samples - when randomly selected -ย canย be representative of populations from which they come, so that by itself isnโt a good reason to say no (the better reason is what you mentioned about the specific fear). You seem to be going for the explanation that there wasnโt random selection, but it doesnโt come across quite as cleanly as you may have wanted. In part ( c ), you give a correct explanation of double-blind. No issues there. :) ย

### 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 the test subjects were volunteers and not obtained randomly, if the โindividuals similar to thoseโ were also volunteers obtained in the same fashion as those volunteers were, only then they can be generalized to them.
c) Double blind means that both the test subjects getting the treatment and the researchers or other people implementing the treatment 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 โgiver of pill peopleโ 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! All three parts include appropriate information, in context. I also appreciate the phrase โgiver of pill peopleโ and may or may not borrow it in the future, lol
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