How do you turn a question into hypotheses?
You will be able to: Define a population proportion and choose a pre-specified alternative.
How do you turn a question into hypotheses?
A club’s old support rate was 50%. Before polling, organizers ask whether support has increased. That direction determines which outcomes count as evidence.
A useful starting point: What does 95% confidence actually describe? →
Words and symbols before equations
- Null hypothesis H₀
- The benchmark parameter claim used to construct the test model.
- Alternative Hₐ
- The population claim for which evidence is sought.
- Null value p₀
- The specific benchmark proportion.
- One-sided test
- Tests an increase or decrease; a two-sided test considers either direction.
What this picture assumes
Synthetic study: a simple random sample without replacement from N=100000 independent units. The chosen sizes satisfy the 10% condition. Real studies require their own design checks. Actual count x is rounded from the requested percentage. Normal z inference is withheld when either null expected count is below 10.
Read the picture in three steps
- Read the axes and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- z=2; p-value=0.02275. At α=0.05, reject H₀. Alternative: p > 0.5. This does not give P(H₀).
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the mathematics
Let p be the true proportion of all current club members supporting the proposal. Write H₀:p=.50 and Hₐ:p>.50 for an increase. Hypotheses refer to p, not to the already observed p̂.
For a decrease use <; for any change use ≠. Choose the direction from the research question before seeing the data, rather than picking the smaller tail afterward.
A one-sample z-test can assess this binary population proportion when its conditions hold. In AP work a one-sided null is tested at its boundary equality. The null is an assumption for calculation, not a proven truth.
A worked example, step by step
A delivery team asks whether its late-delivery share differs from .10. Define hypotheses.
- Define p as the current population proportion of that team’s deliveries that arrive late.
- The benchmark is p₀=.10.
- Write H₀:p=.10.
- Because “differs” includes either direction, use Hₐ:p≠.10 and a two-sided test if conditions hold.
Do not write hypotheses about the sample proportion or choose the direction after observing it.
Does p̂=.58 mean the hypothesis is Hₐ:p̂>.50?
Compare with an explanation
No. The hypothesis concerns the unknown population p.
Predict. Change one thing. Explain.
Switch the alternative while keeping the data fixed. Explain why a greater-than research question uses a different tail from a two-sided one.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
z=2; p-value=0.02275. At α=0.05, reject H₀. Alternative: p > 0.5. This does not give P(H₀).
| Quantity | Value |
|---|---|
| Observed successes x | 60 |
| Observed failures n−x | 40 |
| Actual p̂=x/n | 0.6 |
| Null quantity | Value |
|---|---|
| Expected successes | 50 |
| Expected failures | 50 |
| SE under H₀ | 0.05 |
Synthetic study: a simple random sample without replacement from N=100000 independent units. The chosen sizes satisfy the 10% condition. Real studies require their own design checks. Actual count x is rounded from the requested percentage. Normal z inference is withheld when either null expected count is below 10.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using the probability values, reference groups, graph scales or model assumptions. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionBefore an SRS, a council asks whether more than 60% of all students prefer option A. Define p and both hypotheses.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: p is the proportion of all students preferring A.
- 1 point: H₀:p=.60.
- 1 point: Hₐ:p>.60.
- 1 point: The greater-than direction is set before the sample and concerns the population, not p̂.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What belongs in hypotheses?
Population parameters.
RECALL 2When should the alternative be chosen?
Before examining the outcome data.
RECALL 3Which symbol makes a test two-sided?
≠.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How do you turn a question into hypotheses?
- H₀:p=p₀.
- Hₐ:p<p₀, p>p₀ or p≠p₀.
- Define population and success before calculating.
Remember: Do not write hypotheses about the sample proportion or choose the direction after observing it.
Conditions: Synthetic study: a simple random sample without replacement from N=100000 independent units. The chosen sizes satisfy the 10% condition. Real studies require their own design checks. Actual count x is rounded from the requested percentage. Normal z inference is withheld when either null expected count is below 10.
Refresh Kid · AP Statistics Unit 3 · Objectives 3.5.A, 3.5.B · Review edition
Framework, scope and review status
Mapped to College Board, AP Statistics CED, Topic 3.5, objectives 3.5.A, 3.5.B. Framework effective Fall 2026, checked September 17, 2026. Unit 3 includes inference for one and two population proportions, errors and power, and chi-square homogeneity/independence tests; it is part of the revised five-unit course.
Examples and datasets are synthetic, independently authored teaching material. Inference requires a justified design and appropriate counts. Intervals use observed proportions; null tests use their reference-model proportions. The revised CED states chi-square expected counts should be greater than 5; this unit follows that wording even though some companion texts use at least 5. Normal and chi-square inference are approximate. The chi-square goodness-of-fit test is not included in this unit’s official scope.
The Organic Chemistry Tutor companion title and destination were located; the full video was not reviewed. Khan Academy’s destination was checked, but its lesson content was not fully readable by the research tool. OpenStax provides optional reference reading. No provider scripts, questions or graphics were copied. Refresh Kid is not affiliated with these providers.
GitHub’s 3D website collection informed optional spatial inspection. Our original categorical count grid uses self-hosted Three.js with its MIT license. Two rows and three columns organize synthetic people into categorical cells. Each stacked block represents one person. Camera rotation changes only the view; exact counts, expectations and contributions are always available in the 2D table. Inference curves and intervals remain 2D; use the exact table rather than apparent 3D size for comparisons. Complete labeled diagrams, count tables and explanations remain available without 3D.
Independent teacher review and observation of students remain pending. Technical checks do not certify statistical accuracy, accessibility or learning effectiveness. This is a review edition.
Released AP Statistics questions and scoring guides are optional. Older exams use the earlier framework, so check alignment before selecting parts. All practice on this page is original, not official AP material.
Learn → Explore → Practice → Review is informed by the IES learning guide. This implementation has not yet been evaluated with learners.
Want to work through this with a tutor?
Bring your question about How do you turn a question into hypotheses? Your explanation and answers remain free to access.