A hypothesis test (significance test) is an inference procedure that uses sample data to decide between a null hypothesis (H₀) and an alternative hypothesis (Hₐ) about a population parameter, by computing a test statistic and comparing its p-value to a significance level α.
A hypothesis test is the statistical version of "innocent until proven guilty." You start by assuming the null hypothesis (H₀) is true. That's the boring, no-effect claim, like H₀: p = 0.5 or H₀: μ = 122 or H₀: β = 0. Then you collect sample data and ask one question. If H₀ really were true, how surprising would results like mine be? That surprise level is the p-value. If the p-value is at or below your significance level α, you reject H₀ and have convincing evidence for the alternative hypothesis (Hₐ). If the p-value is above α, you fail to reject H₀. You never "accept" or "prove" either hypothesis.
On the AP exam, every hypothesis test follows the same four-part structure no matter which parameter you're testing. State hypotheses and identify the procedure, check conditions, calculate the test statistic and p-value, and conclude in context by comparing the p-value to α. The test statistic itself is always built the same way, as (sample statistic minus null value) divided by the standard deviation (or standard error) of the statistic. Swap in proportions and you get a z-test (Unit 6), swap in means or slopes and you get a t-test (Units 7 and 9), swap in categorical counts and you get a chi-square test (Unit 8). One logic, four costumes.
Hypothesis testing is the backbone of Units 6 through 9, which together make up roughly 35-50% of the AP exam. The CED hits the same three skills for every test type. You calculate the test statistic (AP Stats 6.5.A, 7.5.A, 8.3.A, 9.5.A), interpret the p-value (AP Stats 6.5.B, 7.5.B, 8.3.C, 9.5.B), and justify a claim by comparing the p-value to α (AP Stats 6.6.A, 7.5.C, 8.3.D, 9.5.C). That repetition is the point. Once you can write a complete one-proportion z-test, you already know the skeleton of a two-sample t-test, a chi-square goodness-of-fit test, and a t-test for slope. Topic 6.7 adds the error analysis layer (Type I, Type II, and power), and Topics 7.10 and 9.6 test whether you can pick the right procedure in the first place. If you master the generic logic of a hypothesis test, you've effectively studied four units at once.
Keep studying AP Statistics Unit 7
p-Value (Unit 6)
The p-value is the engine of every hypothesis test. It's the probability, assuming H₀ is true, of getting a test statistic as extreme or more extreme than the one you observed. Every interpretation the CED rewards starts with that "assuming the null is true" clause, whether you're testing a proportion, a mean, or a regression slope.
Type I and Type II Errors (Unit 6)
Every test decision can go wrong in exactly two ways. Rejecting a true H₀ is a Type I error (probability α), and failing to reject a false H₀ is a Type II error (probability 1 − power). Topic 6.7 asks you to describe these errors and their consequences in context, which is a classic FRQ follow-up after you've run a test.
Confidence Interval (Unit 7)
Tests and intervals are two sides of the same inference coin. A test answers "is the parameter equal to this specific value?" while an interval answers "what range of values is plausible for the parameter?" Per Topic 7.3, you can justify the same claim either way. If the null value falls outside a two-sided interval, the matching test would reject H₀.
Chi-Square Statistic (Unit 8)
Chi-square tests prove the hypothesis-test framework isn't just a z and t thing. The statistic looks different, Σ(observed − expected)²/expected with df = categories − 1, but the logic is identical. You still compute a p-value from a null distribution and compare it to α, exactly as in Units 6 and 7.
Test for the Slope of a Regression Model (Unit 9)
Unit 9 closes the course by running a hypothesis test on a Unit 2 idea. Testing H₀: β = 0 asks whether there's a real linear relationship between two quantitative variables in the population. The test statistic t = (b − β)/SEb follows a t-distribution with n − 2 degrees of freedom, and the conclusion structure is the same one you learned for proportions.
Hypothesis tests show up everywhere. Multiple-choice questions love three angles. They ask you to interpret a p-value correctly (the right answer always assumes H₀ is true), identify degrees of freedom or the correct null distribution (like t with n − 2 df for a slope test on 18 observations), and recognize valid conclusions versus traps like "accept the null." On the free-response section, a full significance test is nearly guaranteed. The 2018 FRQ on systolic blood pressure and the 2022 FRQ on teen streaming habits both required a complete test with hypotheses, conditions, mechanics, and a conclusion in context. The 2021 FRQ on a pet-supply coupon experiment tested a difference in proportions. To earn full credit you must define your parameter, state both hypotheses with symbols, name the procedure, verify conditions, report the test statistic and p-value, and write a conclusion that explicitly compares the p-value to α and answers the question in context. Skipping the context or the comparison costs points every year.
Both are inference procedures, but they answer different questions. A hypothesis test makes a yes/no decision about one specific claimed value (reject or fail to reject H₀). A confidence interval estimates a whole range of plausible values for the parameter. They're connected, though. If a null value like p₀ = 0.5 sits outside a 95% confidence interval, a two-sided test at α = 0.05 would reject it. On FRQs, watch the verbs. "Test the claim" means run a test, while "estimate" or "construct an interval" means build a confidence interval.
Every hypothesis test follows the same four steps: state hypotheses and procedure, check conditions, compute the test statistic and p-value, and conclude in context by comparing the p-value to α.
The general test statistic formula is (sample statistic − null parameter value) ÷ standard deviation of the statistic, and it works for z-tests, t-tests, and tests for slope.
If the p-value ≤ α, reject H₀ and conclude there is convincing evidence for Hₐ; if the p-value > α, fail to reject H₀. You never accept or prove a hypothesis.
Every p-value interpretation must include the assumption that the null hypothesis is true; that one clause is what graders look for.
A Type I error rejects a true null (probability α), a Type II error fails to reject a false null, and power is the probability of correctly rejecting a false null.
The same testing logic covers four units: z-tests for proportions (Unit 6), t-tests for means (Unit 7), chi-square tests for categorical counts (Unit 8), and t-tests for regression slopes (Unit 9).
It's a procedure that uses sample data to decide between a null hypothesis (H₀, the no-effect claim) and an alternative hypothesis (Hₐ) about a population parameter. You compute a test statistic, find its p-value assuming H₀ is true, and reject H₀ if the p-value is at or below the significance level α.
No. Failing to reject H₀ only means your sample didn't provide sufficient evidence for the alternative. The null could still be false; you might just have a small sample or low power. Never write "accept H₀" on the exam, because that phrasing loses credit.
A test gives a yes/no decision about one specific claimed parameter value, while a confidence interval gives a range of plausible values for that parameter. They agree with each other. If the null value is outside a 95% interval, a two-sided test at α = 0.05 rejects it.
Match the data type to the test. Categorical data with one or two proportions means a z-test (Unit 6), quantitative data about means means a t-test (Unit 7), counts across multiple categories means chi-square (Unit 8), and a relationship between two quantitative variables means a t-test for slope (Unit 9). Topics 7.10 and 9.6 test this selection skill directly.
Mostly no. The CED explicitly says the test statistic formulas don't appear on the formula sheet but can be built from the general pattern, (statistic − null value) ÷ standard error, using the standard error formulas that ARE on the sheet. Learn the pattern, not twelve separate formulas.