2026 AP Statistics FRQ #2 Explained | Step-by-Step Free Response Question Solution

Hinzugefügt: 2026-05-16

[00:00:00]What's up, my sad stats? Let's talk about question two from the 2026 AP Statistics free response questions. Now, this question was an experimental design problem where we had different rose plants and we're trying to see if adding coffee grounds to the dirt could make the roses, well, grow better or grow more. So, let's take a look at this question right now. It's actually a pretty easy question dealing with collecting data. So, let's take a look at it.

[00:00:22]So, question two starts off with Holly, a botanist, who read an online report that stated that adding coffee grounds to the soil of rose bushes will produce more roses. Holly decides to conduct an experiment to investigate this claim.

[00:00:34]She grows 30 rose bushes in a greenhouse in a controlled experiment or excuse me, controlled environment. So, the conditions will be the same for all rose bushes. When the rose bushes are a month old, she randomly assigns 15 of them to have 1/2 cup of coffee grounds added to their soil weekly and the other 15 rose bushes will have no coffee grounds added to their soil. After 3 months, she counts the number of roses on each rose bush. All right, so part A is pretty straight forward and asks us to identify the treatments, the experimental units, and the response variable. And that's actually pretty quickly to do here. So, the treatments are 1/2 of coffee grounds added to the soil weekly and the second treatment is no coffee grounds added to the soil. The experimental units are the 30 rose bushes in a greenhouse and the soil they're in. Don't know if you have to mention the soil they're in, but technically it's the soil that's actually getting the coffee grounds added to them, but the rose bushes are obviously planted in that soil. And the response variable is the number of roses on each rose bush.

[00:01:32]That's what they're going to actually count at the end of the experiment.

[00:01:36]All right, part B says, "In the context of Holly's experiment, describe how the treatments can be randomly assigned to the experimental units so that each treatment has the same number of units."

[00:01:45]All right, here's what I said. To randomly assign the two treatments to the 30 rose bushes, I would follow the procedure below. Give each rose bush a number, 01 through 30. Use a random number generator to select 15 numbers, ignoring repeats and numbers that not are used. You know, if the number 49 comes up, the rose bush has it, so ignore it. And then the 15 rose bushes corresponding to the 15 selected numbers will get the half cup of coffee grounds added weekly to their soil, and the remaining 15 will get no coffee grounds added. So, that's the pretty the simple procedure that you should be used to do that. You could also do the put um you know, 30 numbers on a piece of paper, but they have to be an equal size piece of paper. Got to make sure you say that. Put them into a hat, shake it up. Got to say that. And then select out without replacement. Don't put that number back. And then the first 15 numbers picked, and those corresponding rose bushes will get the um coffee grounds added, and the other 15 will not. That certainly works as well, but you have to have a lot more details in there. Got to make sure you shake it up.

[00:02:47]Got to make sure their size are equal size pieces of paper. And you got to make sure that you do not put the piece of paper back after you select them. But either one works. I think this is pretty straightforward, so I like this answer the best.

[00:02:58]All right. Then part C says, "After the experiment, Holly determines that her results were statistically significant at the.05 level significance."

[00:03:06]Explaining the meaning of statistically significant in this context.

[00:03:10]So, first you do have to remember what statistically significant means. It means that the results that we saw were too extreme to have occurred by chance, meaning that they didn't occur by chance, and the only result is, well, the adding the coffee grounds will actually works. So, here's what I said that I think is a really nice answer, complete answer using that definition.

[00:03:29]So, in this context, statistically significant at the.05 level means that if adding coffee grounds actually had no effect on the number of roses produced, then the probability of obtaining results as extreme as Holly's results just by random chance would be less than 5%. So, what we're saying is that if we were to actually conduct the test, which you did not have to do, the null is that there's no difference between getting coffee grounds and not. And the P value, what is leading us to making our conclusion, would be saying, "Hey, listen, if there was no effect adding coffee grounds to the roses, then the probability of getting the results that Holly obviously got by chance would be less than 5%, which would cause us to reject the null and go with the alternative that adding coffee grounds actually works." So, because the results were statistically significant, Holly has convincing evidence that adding coffee grounds to the soil affects the number of roses produced by the rose bushes. The results were so different they could not have occurred by chance.

[00:04:26]Now, did you have to have all of that to get full credit? Not necessarily, but you should have had some of this idea um incorporating the definition of statistically significant and what that actually means for her results, that adding the coffee grounds actually does affect the number of roses produced because we have that random assignment and because she must have saw a big enough difference that it could not have occurred by chance resulting a very low P value. Now, even though you didn't have to do the test, that all should make sense to you because you guys should know how to do a test in this situation. All right, that's it for question three. Kind of short, kind of simple, not overly too difficult.