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Unit: Significance tests (hypothesis testing)

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Possible mastery points

The idea of significance tests

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Idea behind hypothesis testing

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Examples of null and alternative hypotheses

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P-values and significance tests

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Comparing P-values to different significance levels

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Estimating a P-value from a simulation

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Using P-values to make conclusions

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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

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Introduction to Type I and Type II errors

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Examples identifying Type I and Type II errors

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Introduction to power in significance tests

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Examples thinking about power in significance tests

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Consequences of errors and significance

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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

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Constructing hypotheses for a significance test about a proportion

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Conditions for a z test about a proportion

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Reference: Conditions for inference on a proportion

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Calculating a z statistic in a test about a proportion

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Calculating a P-value given a z statistic

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Making conclusions in a test about a proportion

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Significance test for a proportion free response example

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

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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

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Learn

Writing hypotheses for a significance test about a mean

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Conditions for a t test about a mean

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Reference: Conditions for inference on a mean

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When to use z or t statistics in significance tests

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Example calculating t statistic for a test about a mean

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Using TI calculator for P-value from t statistic

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Using a table to estimate P-value from t statistic

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Comparing P-value from t statistic to significance level

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Free response example: Significance test for a mean

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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.

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