Introduction: Why Hypothesis Testing Matters in AP Statistics

Hypothesis testing is one of the core inference skills in AP Statistics. You’ll use it to determine whether evidence from a sample is strong enough to support a claim about a population.

On the AP exam, hypothesis testing appears in:

• MCQs (multiple-choice probability/inference questions).
• FRQs (full inference setups: hypotheses, test statistic, p-value, conclusion).

This guide — plus RevisionDojo’s inference worksheets, flowcharts, and FRQ practice banks — will give you a step-by-step method for solving any hypothesis test problem.

Step 1: What is a Hypothesis Test?

• Null Hypothesis (H₀): Statement of no effect or no difference.
• Alternative Hypothesis (Hₐ): Statement of what you’re testing for (effect, difference, greater/less).

Example:

• H₀: µ = 50 (no change).
• Hₐ: µ > 50 (increase).

👉 Hypothesis testing asks: Is the sample evidence strong enough to reject H₀?

Step 2: The Four-Step Inference Process

Always write these steps on FRQs (College Board expects them):

1. State → Define parameter + hypotheses (H₀, Hₐ).
2. Plan → Choose correct test + check conditions.
3. Do → Calculate test statistic + p-value.
4. Conclude → Compare p-value to α and interpret in context.

👉 RevisionDojo’s Inference Templates are built around this format.

Step 3: Choosing the Right Hypothesis Test

• One-sample z-test for proportions (when σ known or population proportion).
• One-sample t-test for means (when σ unknown, common in AP Stats).
• Two-sample t-test (compare two independent means).
• Paired t-test (before-and-after studies).
• Chi-square test (categorical data).

👉 Flowchart from RevisionDojo: Proportion? → z-test. Mean, σ unknown? → t-test. Categorical? → χ².

Step 4: Conditions for Inference

Before running a test, check:

• Random sample or random assignment.
• Normal condition: population normal OR large n (CLT).
• Independence: 10% condition if sampling without replacement.

👉 Without conditions, inference results may not be valid.

Step 5: Test Statistic Formulas

For Means (t-Test)

t=xˉ−μ0s/nt = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}

For Proportions (z-Test)

z=p^−p0p0(1−p0)/nz = \frac{\hat{p} - p_0}{\sqrt{p_0(1-p_0)/n}}

• p^\hat{p} = sample proportion
• p0p_0 = hypothesized proportion

👉 RevisionDojo has formula flashcards for quick recall.

Step 6: Understanding p-Values

• p-value: Probability of seeing results as extreme as the sample, if H₀ is true.
• Small p-value (≤ α) → reject H₀.
• Large p-value (> α) → fail to reject H₀.

Example: p = 0.03, α = 0.05 → reject H₀.

👉 On FRQs, always phrase: “Because p < α, we reject H₀. There is convincing evidence that…”

Step 7: Type I and Type II Errors

• Type I Error (α): Rejecting H₀ when it’s true (false positive).
• Type II Error (β): Failing to reject H₀ when it’s false (false negative).

Example:

• Type I: Concluding a new drug works when it doesn’t.
• Type II: Missing a drug that actually works.

👉 AP exam often asks to identify errors in context.

Step 8: One-Tailed vs Two-Tailed Tests

• One-tailed: Hₐ: µ > µ₀ or µ < µ₀ (directional).
• Two-tailed: Hₐ: µ ≠ µ₀ (non-directional).

Example:

• Hₐ: µ ≠ 100 → two-tailed test.
• Hₐ: µ > 100 → one-tailed test.

👉 p-value is doubled in two-tailed tests.

Step 9: Example Hypothesis Test (Step-by-Step)

A company claims their soda cans contain 355 mL. A random sample of 36 cans has x̄ = 352, s = 6. Test at α = 0.05.

1. State

• H₀: µ = 355
• Hₐ: µ < 355

1. Plan

• One-sample t-test. Conditions: random sample, n = 36 (CLT applies).

1. Do

t=352−3556/36=−31=−3.0t = \frac{352 - 355}{6/\sqrt{36}} = \frac{-3}{1} = -3.0

df = 35 → p ≈ 0.002

1. Conclude
   Since p < 0.05, reject H₀. Evidence suggests mean volume < 355 mL.

👉 RevisionDojo has step-by-step worked problems like this with explanations.

Step 10: Hypothesis Testing on the AP Stats Exam

MCQ Example

Survey: 55% support candidate. Hypothesis: H₀: p = 0.5, Hₐ: p ≠ 0.5, n = 100.
z = (0.55 – 0.50) / √(0.5·0.5/100) = 1.0 → p ≈ 0.32 → fail to reject H₀.

FRQ Example

“Students test whether caffeine increases pulse rate. Conduct appropriate test and interpret results.”

Scoring requires:

• Correct hypotheses.
• Test chosen + conditions.
• Test statistic + p-value.
• Conclusion in context.

👉 RevisionDojo’s FRQ bank shows model answers.

Step 11: Study Hacks for Hypothesis Testing

• Memorize the four-step process.
• Always write conditions.
• Sketch distributions when possible.
• Practice identifying Type I & II errors.
• Use RevisionDojo’s inference flowcharts + FRQs for repetition.

Step 12: Common Mistakes to Avoid

• ❌ Forgetting to write hypotheses in terms of parameters (µ, p).
• ❌ Confusing p-value with significance level.
• ❌ Not concluding in context.
• ❌ Using “accept H₀” instead of “fail to reject H₀.”
• ❌ Mixing up one-tailed vs two-tailed tests.

Step 13: The RevisionDojo Advantage

RevisionDojo helps AP Stats students master hypothesis testing with:

• Step-by-step inference guides.
• Calculator tutorials (TI-84, Desmos).
• FRQ practice banks with rubrics.
• Flowcharts for choosing correct tests.

👉 Check out RevisionDojo’s Hypothesis Testing Resources here.

Frequently Asked Questions (FAQs)

Q: Do I always have to use a t-test for means?
A: Yes, unless σ is known (rare in AP Stats).

Q: What’s the difference between significance level and p-value?
A: α is the threshold, p-value is the result. Compare p to α.

Q: Do I need to memorize test statistic formulas?
A: Yes — but calculators also compute them. Show formulas for FRQs.

Q: What if conditions aren’t met?
A: State the issue (e.g., skewed data, small n). Sometimes proceed with caution.

Q: How does RevisionDojo help with hypothesis testing?
A: With worksheets, flashcards, and past FRQ solutions.

Final Thoughts

Hypothesis testing is one of the most tested inference skills in AP Statistics. If you can confidently state hypotheses, check conditions, calculate test statistics, and interpret results in context — you’ll score highly on both MCQs and FRQs.

To master it:

• Practice the four-step process.
• Memorize test setups + formulas.
• Connect p-values to context.
• Use RevisionDojo’s structured practice tools for repetition.

With this approach, you’ll be able to handle any hypothesis test the AP exam throws at you.