AP Statistics Experimental Design: Coffee Grounds and Rosebushes (Step-by-Step)

Direct answer: Holly's coffee-grounds-and-rosebushes experiment is a textbook AP Statistics experimental design question with three parts. In Part A, the treatments are one-half cup of coffee grounds added weekly vs. no coffee grounds; the experimental units are the 30 rosebushes; the response variable is the number of roses on each rosebush after three months. In Part B, random assignment is done by numbering the rosebushes 1–30 and using a random number generator to pick 15 for the coffee-grounds group. In Part C, "statistically significant at α = 0.05" means the observed difference is unlikely (less than a 5% chance) to have happened by random chance alone if coffee grounds truly had no effect. That's evidence that the treatment matters.

The question (Question 2)

Reproduced from the card above:

2. Holly, a botanist, read an online report that stated that adding coffee grounds to the soil of rosebushes will produce more roses. Holly decides to conduct an experiment to investigate this claim. She grows 30 rosebushes in a greenhouse with a controlled environment so the conditions will be the same for all rosebushes.

When the rosebushes are a month old, she randomly assigns 15 rosebushes to have one-half cup of coffee grounds added to their soil weekly. The other 15 rosebushes will not have coffee grounds added to their soil.

After three months, she counts the number of roses on each rosebush.

(botanist: a scientist who studies the biology of plants)

This is exactly the kind of free-response question that opens an AP Statistics exam — short prose, real-world setup, and three subparts that test whether you've internalized the vocabulary of experimental design. The reason it shows up so often is that it's designed to be quick to score: each subpart asks for one specific concept, and the rubric awards points for naming the right words in the right places.

Part A — Treatments, experimental units, response variable

This is the vocabulary part. Three quick definitions, three quick answers.

i. Treatments

The treatments are what's being applied to the experimental units. There are two here: one-half cup of coffee grounds added weekly, and no coffee grounds added. A common student error is to write "coffee grounds" as the single treatment — but the experimental comparison requires both treatments to be named explicitly, including the control.

ii. Experimental units

The experimental units are what receives the treatment. Here that's the 30 rosebushes. Note that the rosebushes themselves are the units, not the soil or the coffee grounds or the greenhouse. The unit is the thing that gets randomly assigned and measured.

iii. Response variable

The response variable is what gets measured to detect a treatment effect. Here it's the number of roses on each rosebush after three months. "Roses" alone isn't precise enough — the response variable is a count, and the timing matters. Always include both the quantity and the measurement window.

Part B — Random assignment, in the context of this experiment

Part B is where the AP Stats rubric rewards specificity. The question says "describe how the treatments can be randomly assigned." A vague answer ("flip a coin" or "randomly assign them") will not score. The rubric wants a procedure that another student could follow exactly.

Here's the model answer:

Number the 30 rosebushes from 1 to 30. Use a random number generator (or draw slips of paper from a hat) to select 15 numbers without replacement, between 1 and 30. The 15 rosebushes whose numbers are selected receive one-half cup of coffee grounds added to their soil weekly. The remaining 15 rosebushes receive no coffee grounds. This ensures each treatment group has exactly the same number of experimental units (15 per group) and that assignment is determined by chance alone.

Three elements have to be there: (1) a labeling step (number the rosebushes), (2) a named random mechanism (RNG, random number table, slips of paper from a hat — not just "randomly"), and (3) an explicit assignment of who gets which treatment. If any one of those is missing, the rubric strips the point.

Part C — Statistical significance at α = 0.05

This is the conceptual question. The rubric here is testing whether students can translate "statistically significant at α = 0.05" into plain language — without falling into one of the two classic traps.

Model answer:

"Statistically significant at α = 0.05" means that the observed difference in the number of roses between the coffee-grounds group and the no-coffee-grounds group is unlikely to have happened by random chance alone if coffee grounds truly had no effect on rose production. Specifically, there is less than a 5% probability of observing a result this extreme under the assumption that coffee grounds have no effect. In the context of Holly's experiment, this means there is strong evidence that adding coffee grounds changes — and in her data, increases — the number of roses produced by rosebushes.

The two traps students fall into on Part C

• Trap 1: "There is a 5% chance the results are due to chance." This sentence sounds right and is wrong. The 5% is the probability of observing this result given the null hypothesis is true — not the probability that the null hypothesis is true. This is the most common AP Stats error, and the rubric is sharp on it.
• Trap 2: "Coffee grounds cause more roses." The word "cause" is fine here because Holly used random assignment in a controlled experiment — but students should still phrase the conclusion in terms of evidence ("strong evidence that coffee grounds change the number of roses") rather than absolute fact. AP Stats rewards humility about uncertainty.

Why random assignment turns this into a causal claim

Step back from the FRQ for a second. The reason Holly can say "coffee grounds cause more roses" (rather than just "coffee grounds are associated with more roses") is the random assignment. Here's why that matters.

Without random assignment, any difference between the two groups could be explained by some lurking variable — maybe the rosebushes that ended up in the coffee-grounds group happened to get a little more light, or were genetically slightly hardier. With random assignment, those lurking variables are balanced out across the two groups in expectation. So if there's still a meaningful difference in the response variable after three months, the treatment is the most defensible explanation.

This is the single most important conceptual idea in AP Statistics experimental design. Memorize it.

What this question reveals about how the AP Stats rubric thinks

Three patterns show up across every AP Stats experimental-design FRQ:

1. Vocabulary precision is non-negotiable. "Treatment" means a specific thing. "Experimental unit" means a specific thing. "Response variable" means a specific thing. Students who use these words loosely lose points even when their underlying reasoning is correct.
2. Random assignment must be described in concrete steps. The rubric wants a procedure another statistician could replicate, not a hand-wave.
3. Statistical significance is always interpreted "in the context of the experiment." Generic textbook definitions don't score. The rubric wants the answer to reference Holly, the rosebushes, and the rose count specifically.

How we teach AP Statistics at SOMATH

If you've read this far, the question becomes practical: how do you actually get a 5 on the AP Statistics exam? Here's the SOMATH approach to AP Stats experimental design specifically — and to the exam more broadly.

1. Drill the vocabulary first. Treatments, experimental units, response variable, explanatory variable, factor, level, block, control group, placebo, random assignment, random sampling, lurking variable, confounding variable. These should be reflexes. We use a one-page sheet our AP Stats students keep with them through the whole experimental-design unit.
2. Use only released AP questions as training material. There are 25 years of College Board free-response questions in the public archive. The patterns repeat. We work through 3–4 FRQs per week and write answers in rubric-aware language from day one — no vague "kind of significant" or "more or less random."
3. Practice the rubric, not just the math. AP Stats is unusual among AP exams in that the rubric rewards how you explain as much as what you compute. Our students grade each other's free responses using the actual scoring guidelines before they ever turn one in to a teacher. By exam day, they know exactly which words trigger points and which ones lose them.

That's the entire system. The students who follow it score 4s and 5s. The students who memorize formulas without practicing rubric-aware language often score 3s and 2s — and then they're surprised. Don't be surprised. AP Statistics is a writing exam dressed in mathematical notation.

FAQ

What are the treatments, experimental units, and response variable in Holly's coffee grounds experiment?

Treatments: one-half cup of coffee grounds added weekly vs. no coffee grounds added. Experimental units: the 30 rosebushes. Response variable: the number of roses on each rosebush after three months.

How do you randomly assign 15 rosebushes to each group on the AP Statistics exam?

Number the 30 rosebushes 1–30. Use a random number generator (or slips of paper drawn from a hat) to select 15 numbers without replacement. Those 15 rosebushes receive one-half cup of coffee grounds weekly; the remaining 15 receive no coffee grounds. The AP Stats rubric requires a named random mechanism — not just "randomly assigned."

What does "statistically significant at α = 0.05" mean in plain English?

It means the observed difference between groups is unlikely (less than 5% probability) to have happened by random chance alone if the treatment truly had no effect. In Holly's experiment, it's strong evidence that coffee grounds change — and in her data, increase — the number of roses produced.

Why is random assignment so important in experimental design?

Random assignment balances out lurking variables (light, soil pH, watering quirks) across the two treatment groups, so any post-treatment difference in the response variable can be attributed to the treatment itself. Without random assignment, the conclusion "coffee grounds caused more roses" isn't defensible.

Do you offer AP Statistics tutoring on the Upper West Side?

Yes — AP Statistics is one of our core AP programs. We tutor it year-round and offer intensive May-exam prep cycles each spring. Our entire program operates from 226 W 79th St on the Upper West Side. Math tutoring UWS is the core of what we do.

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