Introduction
One of the biggest score-killers on AP Statistics FRQs is writing weak or incomplete conclusions. Even if you run all the correct calculations, failing to state your conclusion in context can cost you crucial points.
In fact, the College Board explicitly requires students to write conclusions in non-technical, plain English that clearly answer the research question.
This article will show you:
- How to structure conclusions for confidence intervals and significance tests
- Common conclusion mistakes students make
- Templates you can use on exam day
- Sample conclusions from real AP Stats-style problems
By the end, you’ll know exactly how to lock in those last points on every FRQ.
1. Why Conclusions Matter on the AP Stats Exam
- Each inference question has a “Communicate” point for writing the conclusion.
- Without this, you can’t earn full credit—even if your math is flawless.
- The conclusion must be:
- In context (mention the scenario)
- Linked to confidence intervals or p-values
- Clear and unambiguous
✅ Key Tip: Always imagine you are explaining the result to someone who has never taken statistics.
2. Structure of a Good AP Stats Conclusion
No matter the question type, your conclusion should include:
- Restating the parameter: Remind the reader what you were estimating or testing.
- Connecting to the result: Mention the interval or p-value.
- Decision/interpretation: Say whether it supports or rejects the claim.
- Context: Tie everything back to the real-world problem.
3. Conclusions for Confidence Intervals
Template
“We are ___% confident that the true [parameter in context] is between [lower bound] and [upper bound].”
✅ Example:
A 95% confidence interval for the mean SAT math score at a school is (510, 540).
- Conclusion: “We are 95% confident that the true mean SAT math score for all students at this school is between 510 and 540.”
⚠️ Common Mistake:
- Saying “There is a 95% chance the mean is in the interval.”
- The mean is fixed—the interval captures it 95% of the time.
4. Conclusions for Significance Tests
Template
- If p ≤ α (reject null):
“Since the p-value is less than α, we reject the null hypothesis. There is convincing evidence that [state alternative in context].” - If p > α (fail to reject null):
“Since the p-value is greater than α, we fail to reject the null hypothesis. There is not convincing evidence that [state alternative in context].”
✅ Example:
A study tests whether a new tutoring program improves math scores.
- H0:μ=500H_0: μ = 500
- Ha:μ>500H_a: μ > 500
- p-value = 0.03, α = 0.05
Conclusion: “Since the p-value (0.03) is less than α = 0.05, we reject the null hypothesis. There is convincing evidence that the tutoring program increases mean math scores.”
5. Linking Conclusions to the Real-World Context
Always mention the population and variable from the problem.
- Wrong: “We reject the null hypothesis.”
- Right: “We reject the null hypothesis. There is convincing evidence that the average commute time for students at this school is greater than 30 minutes.”
✅ Use keywords from the prompt in your conclusion.
6. How to Handle “Not Significant” Results
Students often struggle here. You must avoid overclaiming.
- Wrong: “We proved the null is true.”
- Right: “We fail to reject the null. There is not convincing evidence that the mean commute time is greater than 30 minutes.”
Remember: Failing to reject is not the same as proving the null.
7. Special Case: Comparing Two Groups
If your test compares two means or proportions, always phrase your conclusion in terms of the difference.
✅ Example:
A 95% CI for μmen−μwomenμ_{men} - μ_{women} is (−2.5, 1.0).
- Conclusion: “We are 95% confident that the true difference in mean running times (men − women) is between −2.5 minutes and 1.0 minute. Since the interval includes 0, there is not convincing evidence of a difference in average running times.”
8. AP Stats Exam Tips for Conclusions
- Always state in words what the interval/test shows.
- Use “convincing evidence” phrasing (College Board loves this).
- Never say “accept the null”—instead say “fail to reject.”
- Practice writing in clear, complete sentences.
9. Common Mistakes Students Make
- ❌ Forgetting context (“We reject the null” without explaining the scenario)
- ❌ Misinterpreting a CI as probability about the parameter
- ❌ Saying “accept the null” instead of “fail to reject”
- ❌ Leaving out the significance level or confidence level
- ❌ Using technical jargon instead of plain English
10. Sample AP Stats Conclusion Practice
Question:
Researchers want to know if a new fertilizer increases crop yield.
- H0:μ=200H_0: μ = 200 bushels
- Ha:μ>200H_a: μ > 200 bushels
- Sample mean = 205, p-value = 0.07, α = 0.05
Conclusion:
“Since the p-value (0.07) is greater than α = 0.05, we fail to reject the null hypothesis. There is not convincing evidence that the new fertilizer increases average crop yield above 200 bushels.”
11. Last-Minute Exam Strategies
- Before writing, underline the context (population & variable).
- Memorize the templates for CI and significance test conclusions.
- Always end with a sentence in context (who/what the result is about).
- On FRQs, conclusions are often worth 1–2 easy points—don’t give them away!
Conclusion
Writing strong conclusions in AP Statistics FRQs is the difference between a 4 and a 5. The math gets you most of the way, but the conclusion shows the College Board that you understand how statistics applies to real-world problems.
By practicing with these templates and examples, and reviewing guides from RevisionDojo, you’ll never lose points for weak conclusions again.
Frequently Asked Questions
Q: Do I always need to write a conclusion in context?
A: Yes—without context, you won’t earn the “Communicate” point.
Q: Should I include the exact p-value in my conclusion?
A: Yes, if provided. If not, you can state it as “small” or “large.”
Q: Is it okay to say ‘accept the null’?
A: No—always say “fail to reject the null.”
Q: What’s the difference between ‘convincing evidence’ and ‘not convincing evidence’?
A: “Convincing evidence” means rejecting the null. “Not convincing evidence” means failing to reject.
Q: How many sentences should my conclusion be?
A: Typically 2–3 complete sentences is enough.
