Well, here’s my first draft of possible solutions.
Disclaimer: I construct these as a service for both students and teachers to start discussions. There is nothing “official” about these solutions. I certainly can’t even guarantee that they are correct. They probably have typos and errors. If you catch some, let me know! But if they generate discussion and help others, then I’ve succeeded.
The link to my solutions is here: Possible Solutions 2015 AP FRQ
Thoughts about the questions:
#1. Part a was straightforward. Part b will require students to construct a pretty sophisticated criterion for preferring either company. It will be interesting to see how “convincing” students’ arguments need to be.
#2. A great, simple question that will require precise communication of how confidence intervals work. I like how students must explain why a lack of evidence for claim does not imply evidence that its negation is true.
#3. This should, hopefully, be a slam dunk for kids. This is a good indicator of whether your students are understanding the formulas you use, or simply mimicking things that were done in previous problems.
#4. A straight up inference test for the difference in two population proportions. I anticipate students not being specific enough in stating that volunteers were randomly assigned to treatments.
#5. Again a great litmus test to see if students understand the tools they use. This seems almost too simple for #5.
#6. I think that this was a great, challenging problem. It’s a great problem to use in teaching sampling distributions in the future. It requires students to consider the distribution of a population, the distribution from a sample from that population, and the distribution of the sampling distribution of the sample means. I especially like how the oft-ignored requirement of simple random sampling comes to the surface here. I worry that too many students will overlook the questions posed and write something that is simplistic and irrelevant.