Introduction: Why Practice Problems Matter
The AP Statistics exam isn’t just about memorizing formulas — it’s about applying statistical reasoning to real-world problems. The best way to prepare? Practice problems with detailed explanations.
This guide compiles high-yield AP Statistics problems (both multiple-choice and free-response style), with step-by-step solutions so you can see exactly how to approach them.
Every example follows the structure expected by AP graders and pairs with RevisionDojo’s practice hubs for deeper study.
Problem 1: Interpreting a Scatterplot (Unit 2)
Question:
A scatterplot shows the relationship between hours studied and AP Statistics scores. The correlation is r = 0.82. Which is the best interpretation?
- A) Hours studied causes higher scores.
- B) Strong positive linear relationship between hours studied and scores.
- C) Outliers make the correlation invalid.
- D) A correlation of 0.82 means 82% of score variation is explained by studying.
Correct Answer: B
Explanation: Correlation describes strength and direction, not causation. Option D confuses correlation with r².
👉 Practice this type with RevisionDojo’s Correlation & Regression Hub.
Problem 2: Sampling Method (Unit 4)
Question:
A school wants to survey 200 students out of 2,000. They randomly select 20 classes and survey everyone in those classes. What sampling method is this?
- A) SRS
- B) Stratified
- C) Cluster
- D) Convenience
Correct Answer: C (Cluster)
Explanation: Entire clusters (classes) are chosen randomly, and all members are surveyed.
Problem 3: Probability with Cards (Unit 5)
Question:
What is the probability of drawing 2 hearts in a row without replacement from a standard deck?
Solution:
- P(1st heart) = 13/52.
- P(2nd heart) = 12/51.
- Multiply → (13/52)(12/51) = 156/2652 = 0.059.
Answer: 0.059 (≈ 5.9%).
👉 RevisionDojo’s Probability Practice Hub has hundreds of card/dice problems.
Problem 4: One-Sample Proportion Test (Unit 6)
Question:
A company claims 60% of customers are satisfied. In a sample of 100, 52 are satisfied. Test H₀: p = 0.60 vs Hₐ: p ≠ 0.60 at α = 0.05.
Solution:
- p̂ = 52/100 = 0.52.
- z = (0.52 – 0.60) / √[(0.6)(0.4)/100] = -1.63.
- p-value = 0.103.
- Since p = 0.103 > 0.05, fail to reject H₀.
Conclusion: Not enough evidence that satisfaction differs from 60%.
👉 RevisionDojo provides step-by-step calculator guides for z-tests.
Problem 5: Confidence Interval (Unit 7)
Question:
Construct a 95% confidence interval for μ given: x̄ = 84, s = 12, n = 36.
Solution:
- SE = 12 / √36 = 2.
- t* ≈ 2.03 (df = 35).
- Margin of error = 2.03 × 2 = 4.06.
- CI = 84 ± 4.06 → (79.94, 88.06).
Answer: (79.9, 88.1).
Interpretation: We are 95% confident the true mean lies between 79.9 and 88.1.
Problem 6: Chi-Square Test (Unit 8)
Question:
A die is rolled 120 times. Expected counts are 20 per face. Results: [15, 25, 18, 22, 20, 20]. Conduct χ² test for fairness.
Solution:
- χ² = Σ (O-E)² / E = [(15-20)²/20] + … = 3.5.
- df = 5. p ≈ 0.62.
- Fail to reject H₀ → no evidence die is unfair.
👉 RevisionDojo’s Chi-Square Hub provides more worked examples.
Problem 7: FRQ-Style (Regression)
Question:
A regression of GPA on study hours gives slope = 0.12, SE = 0.04, n = 40. Test H₀: slope = 0 vs Hₐ: slope > 0.
Solution:
- t = (0.12 – 0) / 0.04 = 3.0.
- df = 38. p ≈ 0.002.
- Reject H₀. Evidence that study hours positively predict GPA.
FRQ Tip: Always interpret in context!
How to Use These Problems for Practice
- Step 1: Attempt without looking at solution.
- Step 2: Check answer and explanation.
- Step 3: Write out reasoning in full sentences.
- Step 4: Redo similar problems on RevisionDojo.
RevisionDojo Resources for Practice
- Question banks for each unit.
- Timed quizzes (MCQ + FRQ).
- Step-by-step solutions with rubrics.
- Error analysis tools to track weak spots.
👉 Check out RevisionDojo’s AP Statistics Practice Hub here.
Frequently Asked Questions (FAQs)
Q: Are AP Statistics practice problems more important than review books?
A: Yes — practicing problems in AP format is the best prep.
Q: Should I focus more on FRQs or MCQs?
A: Both — but FRQs require more writing skill, so they need extra practice.
Q: Do I need to show calculator steps on the exam?
A: No — just state test name, conditions, and results.
Q: How many practice problems should I do before the exam?
A: At least 300 MCQs and 15–20 FRQs.
Q: Where can I find practice with full explanations?
A: RevisionDojo’s Practice Hub has worked-out solutions and rubrics.
Final Thoughts
The AP Statistics exam rewards students who practice in exam conditions with full explanations. By working through problems like these and using RevisionDojo’s targeted tools, you’ll develop the reasoning, writing, and calculator skills to score a 4 or 5.
Remember: Don’t just memorize formulas — practice applying them to real-world data and writing clear conclusions. That’s the difference between a 3 and a 5.
