Top AP Statistics Practice Problems with Explanations | 2025 Prep

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%).

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%.

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.

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.

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.