A significance test starts with two competing claims about a population proportion: the null hypothesis (no change, the claimed value) and the alternative (what the researcher suspects). Build the setup for real situations and get instant feedback.
Read the situation, then build the test: define the parameter, write the null and alternative hypotheses, pick α, and check the conditions. Press Check my setup for feedback.
The null is the claim of no change or no difference. We assume it is true and ask whether the data are surprising under it.
The alternative is what the researcher suspects. One-sided (< or >) for a directional suspicion; two-sided (≠) for "different" or "changed."
Define p in context: "the true proportion of all … who …". Never write hypotheses with p̂.
α is the cutoff for how unlikely the data must be under H₀ before we reject it. Common choices: 0.05, 0.01, 0.10.
Random sample or random assignment; n ≤ 10% of the population; np₀ ≥ 10 and n(1 − p₀) ≥ 10, using the null value.
If H₀ is true and conditions hold, p̂ has an approximately normal distribution centered at p₀. That's the yardstick for the test.
Turning words into hypotheses.
| Wording in the problem | Alternative | Example |
|---|---|---|
| more than, higher, increased, exceeds | Hₐ: p > p₀ | "Is the defect rate higher than 3%?" → Hₐ: p > 0.03 |
| less than, lower, decreased, fewer | Hₐ: p < p₀ | "Has texting decreased from 22%?" → Hₐ: p < 0.22 |
| different, changed, not equal, fair? | Hₐ: p ≠ p₀ | "Is the coin unfair?" → Hₐ: p ≠ 0.5 |
| The claimed or historical value | H₀: p = p₀ | "The company claims 95%." → H₀: p = 0.95 |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 3.5. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 3 terminology guide.