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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)
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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)
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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)
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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)
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
Conditions for a t test about 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.
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