If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Main content

Unit: Significance tests (hypothesis testing)

AP Stats:

DAT (BI)

,

DAT‑3 (EU)

,

UNC (BI)

,

UNC‑5 (EU)

,

VAR (BI)

,

VAR‑6 (EU)

,

VAR‑7 (EU)

0

Possible mastery points

The idea of significance tests

AP Stats:

DAT (BI)

,

DAT‑3 (EU)

,

DAT‑3.A (LO)

,

DAT‑3.A.1 (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.6 (EK)

,

DAT‑3.B.7 (EK)

,

DAT‑3.E (LO)

,

DAT‑3.E.1 (EK)

,

DAT‑3.F (LO)

,

DAT‑3.F.1 (EK)

,

DAT‑3.F.2 (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.G (LO)

,

VAR‑6.G.4 (EK)

,

VAR‑7 (EU)

,

VAR‑7.C (LO)

,

VAR‑7.C.1 (EK)

Learn

Idea behind hypothesis testing

(Opens a modal)

Examples of null and alternative hypotheses

(Opens a modal)

P-values and significance tests

(Opens a modal)

Comparing P-values to different significance levels

(Opens a modal)

Estimating a P-value from a simulation

(Opens a modal)

Using P-values to make conclusions

(Opens a modal)

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!

Error probabilities and power

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 errors

(Opens a modal)

Examples identifying Type I and Type II errors

(Opens a modal)

Introduction to power in significance tests

(Opens a modal)

Examples thinking about power in significance tests

(Opens a modal)

Consequences of errors and significance

(Opens a modal)

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!

Quiz 1

Level up on the above skills and collect up to 400 Mastery points

Testing hypotheses about a proportion

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 proportion

(Opens a modal)

Conditions for a z test about a proportion

(Opens a modal)

Reference: Conditions for inference on a proportion

(Opens a modal)

Calculating a z statistic in a test about a proportion

(Opens a modal)

Calculating a P-value given a z statistic

(Opens a modal)

Making conclusions in a test about a proportion

(Opens a modal)

Significance test for a proportion free response example

(Opens a modal)

Significance test for a proportion free response (part 2 with correction)

(Opens a modal)

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!

Quiz 2

Level up on the above skills and collect up to 500 Mastery points

Testing hypotheses about a mean

AP Stats:

DAT (BI)

,

DAT‑3 (EU)

,

DAT‑3.E (LO)

,

DAT‑3.E.1 (EK)

,

DAT‑3.F (LO)

,

DAT‑3.F.1 (EK)

,

DAT‑3.F.2 (EK)

,

VAR (BI)

,

VAR‑7 (EU)

,

VAR‑7.B (LO)

,

VAR‑7.B.1 (EK)

,

VAR‑7.C (LO)

,

VAR‑7.C.1 (EK)

,

VAR‑7.D (LO)

,

VAR‑7.D.1 (EK)

,

VAR‑7.E (LO)

,

VAR‑7.E.1 (EK)

Learn

Writing hypotheses for a significance test about a mean

(Opens a modal)

Conditions for a t test about a mean

(Opens a modal)

Reference: Conditions for inference on a mean

(Opens a modal)

When to use z or t statistics in significance tests

(Opens a modal)

Example calculating t statistic for a test about a mean

(Opens a modal)

Using TI calculator for P-value from t statistic

(Opens a modal)

Using a table to estimate P-value from t statistic

(Opens a modal)

Comparing P-value from t statistic to significance level

(Opens a modal)

Free response example: Significance test for a mean

(Opens a modal)

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!

Quiz 3

Level up on the above skills and collect up to 500 Mastery points

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 1400 Mastery points!

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.