IB Maths AI 4.13 Notes

This page contains our IB Maths AI notes for 4.13. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Distribution tests'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Introduction To Linear Statistics 4.5: Probability 4.6: Probability Distributions 4.7: Hypotheses & Tests (HL)4.8: Data collection & categorisation (HL)4.9: Advanced linear statistics (HL)4.10: Linear transformations & combinations (HL)4.11: Confidence intervals (HL)4.12: Poisson distribution (HL)4.13: Distribution tests (HL)4.14: Transition matrices

Checking your access to read these notes...

Chapters

1. Critical values

2. Tests for population means & correlation

3. Binomial test

4. Poisson tests

5. Type I & Type II errors

Loading progress...

Critical values

In this section, we extend hypothesis testing to a wider range of distributions. We look at critical values and critical regions, tests for a population mean, tests for a population proportion, tests using the Poisson distribution, tests for correlation, and the meaning of Type I and Type II errors.

A critical region is the set of values of the test statistic that leads us to reject $H_0$ . A critical value is the boundary of this region.

If the test statistic falls inside the critical region, we reject $H_0$ .
If it does not, we do not reject $H_0$ .

The size of the critical region is chosen so that the probability of rejecting $H_0$ when it is true is at most the significance level.

For a one-tailed test, the critical region lies in one tail of the distribution.
For a two-tailed test, the critical region is split between both tails.

tibertutor.com

Next Up

You have completed the sub-topic 4.13 notes, covering "Distribution tests" for IB Maths AI - continue with related resources below or explore the full IB Maths AI course from the IBO.

Other Sub-topic 4.13 resources