Statistics Option

IB Higher Level Mathematics : Option

9. Statistics

9.1

Poisson distribution: mean and variance (without proof).

The Poisson Distribution has an explanation and an example in the form of a JAVA applet.

There is a Mathematica lab on the Poisson distribution at Search for Problem Sets.
Click the Probability link.

9.2

Mean and variance of linear combinations of two independent random variables.

9.3

Sampling distribution of the mean. Standard error of the mean. Central limit theorem (without proof). Pooled estimators of population parameters for two samples.

For background material, see Sampling Distributions, one of several Introductory Statistics Demonstrations from Ohio University's Department of Psychology.

Also see the Sampling Distribution entry in the Statistics Glossary.

9.4

Finding confidence intervals for the mean of a normal population from a sample.

See Confidence Interval, from the extensive Eric's Treasure Trove of Mathematics site.

Also see the Confidence Interval for a Mean entry in the Statistics Glossary.

9.5

Significance testing: the mean of a sample; the difference between two means. Null and alternative hypotheses H₀ and H₁. Significance levels; critical region and critical values; one-tailed and two-tailed tests. Drawing conclusions.

9.6

The c² distribution; degrees of freedom, n. The c² statistic

. The c² goodness of fit test.

See Chi-Squared Test, from Eric's Treasure Trove of Mathematics.

Also see Chi-Square, a lesson from Amar Patel.

9.7

Contingency tables. The c² test for the independence of two factors.