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# Significance tests (hypothesis testing)

AP Stats: DAT (BI), DAT‑3 (EU), UNC (BI), UNC‑5 (EU), VAR (BI), VAR‑6 (EU)

AP Stats: VAR (BI), VAR‑6 (EU), VAR‑6.D (LO), VAR‑6.D.1 (EK), VAR‑6.D.2 (EK), VAR‑6.D.3 (EK), VAR‑6.D.4 (EK), VAR‑6.D.5 (EK), VAR‑6.G (LO), VAR‑6.G.4 (EK)

Learn

Idea behind hypothesis testingExamples of null and alternative hypothesesP-values and significance testsComparing P-values to different significance levelsEstimating a P-value from a simulationUsing P-values to make conclusions

Practice

Writing null and alternative hypothesesGet 3 of 4 questions to level up!

Estimating P-values from simulationsGet 3 of 4 questions to level up!

AP Stats: UNC (BI), UNC‑5 (EU), UNC‑5.A (LO), UNC‑5.A.1 (EK), UNC‑5.A.2 (EK), UNC‑5.B (LO), UNC‑5.B.1 (EK), UNC‑5.B.2 (EK), UNC‑5.B.3 (EK), UNC‑5.C (LO), UNC‑5.C.1 (EK), UNC‑5.D (LO), UNC‑5.D.1 (EK), UNC‑5.D.2 (EK)

Learn

Introduction to Type I and Type II errorsExamples identifying Type I and Type II errorsIntroduction to power in significance testsExamples thinking about power in significance testsConsequences of errors and significance

Practice

Type I vs Type II errorGet 3 of 4 questions to level up!

Error probabilities and powerGet 3 of 4 questions to level up!

AP Stats: DAT (BI), DAT‑3 (EU), DAT‑3.A (LO), DAT‑3.A.1 (EK), DAT‑3.A.2 (EK), DAT‑3.B (LO), DAT‑3.B.1 (EK), DAT‑3.B.2 (EK), DAT‑3.B.3 (EK), DAT‑3.B.4 (EK), DAT‑3.B.5 (EK), DAT‑3.B.8 (EK), DAT‑3.B.9 (EK), VAR (BI), VAR‑6 (EU), VAR‑6.D (LO), VAR‑6.D.1 (EK), VAR‑6.D.2 (EK), VAR‑6.D.3 (EK), VAR‑6.D.4 (EK), VAR‑6.D.5 (EK), VAR‑6.E (LO), VAR‑6.E.1 (EK), VAR‑6.F (LO), VAR‑6.F.1 (EK), VAR‑6.G (LO), VAR‑6.G.1 (EK), VAR‑6.G.2 (EK), VAR‑6.G.3 (EK), VAR‑6.G.4 (EK)

Learn

Constructing hypotheses for a significance test about a proportionConditions for a z test about a proportionReference: Conditions for inference on a proportionCalculating a z statistic in a test about a proportionCalculating a P-value given a z statisticMaking conclusions in a test about a proportionSignificance test for a proportion free response exampleSignificance test for a proportion free response (part 2 with correction)

Practice

Writing hypotheses for a test about a proportionGet 3 of 4 questions to level up!

Conditions for a z test about a proportionGet 3 of 4 questions to level up!

Calculating the test statistic in a z test for a proportionGet 3 of 4 questions to level up!

Calculating the P-value in a z test for a proportionGet 3 of 4 questions to level up!

Making conclusions in a z test for a proportionGet 3 of 4 questions to level up!

AP Stats: DAT (BI), DAT‑3 (EU), DAT‑3.F (LO), DAT‑3.F.1 (EK), DAT‑3.F.2 (EK)

Learn

Writing hypotheses for a significance test about a meanConditions for a t test about a meanReference: Conditions for inference on a meanWhen to use z or t statistics in significance testsExample calculating t statistic for a test about a meanUsing TI calculator for P-value from t statisticUsing a table to estimate P-value from t statisticComparing P-value from t statistic to significance levelFree response example: Significance test for a mean

Practice

Writing hypotheses for a test about a meanGet 3 of 4 questions to level up!

Conditions for a t test about a meanGet 3 of 4 questions to level up!

Calculating the test statistic in a t test for a meanGet 3 of 4 questions to level up!

Calculating the P-value in a t test for a meanGet 3 of 4 questions to level up!

Making conclusions in a t test for a meanGet 3 of 4 questions to level up!

### About this unit

If a basketball player says they make 75% of the shots they take, but they only make 65% of shots in a sample, does that mean they're lying? Significance tests give us a formal process for using sample data to evaluate how plausible a claim about a population value is. We calculate P-values to see how likely sample results are to occur by random chance, and we use P-values to make conclusions about hypotheses.AP® is a registered trademark of the College Board, which has not reviewed this resource.