Introduction: Why Language Matters in Hypothesis Testing
In AP Statistics, it’s not enough to calculate the right numbers.
The exam graders look for precise language when you:
- State hypotheses.
- Check conditions.
- Write conclusions.
The difference between vague and precise wording can cost you points on FRQs.
This guide will show you how to use hypothesis testing language step by step, with RevisionDojo’s templates and examples designed for AP success.
Step 1: State Hypotheses Clearly
Hypotheses are always about population parameters, not statistics.
- Null hypothesis (H₀): No effect, no difference, status quo.
- Alternative hypothesis (Hₐ): What you’re trying to prove (directional or two-sided).
Examples:
- One proportion:
- H₀: p=0.5p = 0.5
- Hₐ: p>0.5p > 0.5
- One mean:
- H₀: μ=75\mu = 75
- Hₐ: μ≠75\mu \neq 75
RevisionDojo tip: Always write hypotheses with symbols and in context.
Step 2: Check Conditions (Assumptions)
Before running a test, check:
- Random: Data is from a random sample or randomized experiment.
- Normal:
- Proportions: np^≥10n\hat{p} \geq 10 and n(1−p^)≥10n(1-\hat{p}) \geq 10
- Means: n≥30n \geq 30 or population normal.
- Independent: 10% condition if sampling without replacement.
On FRQs, don’t just check silently — write them out.
Step 3: Test Statistic and p-Value
AP Stats requires you to show the formula and calculation:
- One-prop z-test:
z=p^−p0p0(1−p0)nz = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} - One-sample t-test:
t=xˉ−μ0s/nt = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}
Then calculate the p-value (probability of observing sample result or more extreme if H₀ is true).
Step 4: Make a Decision
Compare p-value to significance level (α\alpha):
- If p≤αp \leq \alpha: Reject H₀.
- If p>αp > \alpha: Fail to reject H₀.
RevisionDojo tip: Never say “accept H₀.”
Step 5: Write a Conclusion in Context
This is where precise hypothesis testing language matters most.
A good conclusion must include:
- Decision: Reject/fail to reject H₀.
- Evidence level: Reference p-value.
- Context: Population parameter.
Example (AP Style):
“Because the p-value (0.018) is less than α = 0.05, we reject H₀. We have convincing evidence that the true mean time high school students sleep per night is less than 7 hours.”
Hypothesis Testing Language Templates
RevisionDojo provides sentence starters to ensure you never lose points:
- Hypotheses: “Let p = true proportion of …”
- Conditions: “We assume conditions (Random, Normal, Independent) are satisfied.”
- Decision: “Because p-value [< or >] α, we [reject/fail to reject] H₀.”
- Conclusion: “There is [convincing / not convincing] evidence that [parameter in context] …”
Common Mistakes Students Make
- Writing hypotheses about statistics instead of parameters.
- Forgetting to check conditions.
- Saying “accept H₀” instead of “fail to reject.”
- Not including context in conclusion.
- Misinterpreting p-value (thinking it’s probability H₀ is true).
RevisionDojo’s mistake logs help prevent these errors.
Example FRQ Walkthrough
Scenario: A teacher claims that at least 60% of students do their homework daily. In a random sample of 100 students, 52 said they do. Test at α = 0.05.
- Hypotheses:
- H₀: p=0.60p = 0.60
- Hₐ: p<0.60p < 0.60, where p = true proportion of students who do homework daily.
- Conditions:
- Random: Given.
- Normal: np0=100(0.6)=60≥10np_0 = 100(0.6) = 60 \geq 10; n(1−p0)=40≥10n(1-p_0) = 40 \geq 10.
- Independent: 100 ≤ 10% of population.
- Test statistic:
p^=52/100=0.52\hat{p} = 52/100 = 0.52
SE = 0.6(0.4)100=0.049\sqrt{\frac{0.6(0.4)}{100}} = 0.049
z = 0.52−0.600.049=−1.63\frac{0.52-0.60}{0.049} = -1.63 - p-value: 0.051
- Decision: Since p = 0.051 > α = 0.05, fail to reject H₀.
- Conclusion: There is not convincing evidence that fewer than 60% of students do their homework daily.
RevisionDojo’s Hypothesis Testing Resources
RevisionDojo gives you tools to make hypothesis testing exam-ready:
- Formula sheets for z-tests, t-tests, chi-square, regression.
- Flashcards for p-value interpretations.
- Practice FRQs with scoring guidelines.
- Sentence frames to practice precise language.
Exam-Day Checklist
- Write hypotheses in symbols + words.
- Always check R, N, I conditions.
- Show work for test statistic + p-value.
- Compare p-value to α.
- Write conclusion in full context.
Frequently Asked Questions (FAQs)
Q: Do I have to write hypotheses in symbols?
A: Yes, but also explain them in words.
Q: Can I say “accept H₀”?
A: No. Always say “fail to reject H₀.”
Q: What’s the biggest language trap?
A: Forgetting context — AP graders want the parameter clearly stated.
Q: Do I always need α = 0.05?
A: No, use the level given in the problem.
Q: Is hypothesis testing always one-sided?
A: No, some problems use two-sided tests (≠).
Final Thoughts
Hypothesis testing isn’t just about math — it’s about communication.
On the AP exam, graders reward students who use clear, precise language.
- State hypotheses about parameters.
- Check assumptions (R, N, I).
- Calculate test statistic and p-value.
- Write a decision with α.
- Conclude in context using precise wording.
With RevisionDojo’s sentence frames, practice FRQs, and mistake logs, you’ll develop the exact hypothesis testing language AP graders want — and earn full credit.
