What | Professional Learning for FMU5 (Further Statistics) |

Who | KS5 teachers |

When | March to July 2023 |

How | online |

To book | b.h.denyer@swansea.ac.uk |

**More information**

The course will be run in five self-study sessions:

**Session 1 : Statistical distributions**

The session considers linear combinations of independent normally distributed random variables, the mean of a random sample from a normal distribution with known mean and variance and we also look at the Central Limit Theorem.

**Session 2 : Estimators**

This session focuses on estimators and in particular unbiased estimators and how to choose between them. We look at unbiased estimators of a probability, a population mean and of a population variance along with their standard errors.

**Session 3 : Hypothesis testing (1)**

This session looks at hypothesis tests for:

(a) a specified mean of any distribution whose variance is estimated from a large sample, (b) difference of two means for two independent normal distributions with known variances,

(c) a specified mean of a normal distribution with unknown variance interpreting results for these tests in context.

**Session 4 : Hypothesis testing (2)**

This session focuses on non-parametric tests, i.e. alternative tests for when a distributional model cannot be assumed.

We look at the use of Mann-Whitney and Wilcoxon signed-rank tests, interpreting the results in context.

**Session 5 : Estimation – Confidence Limits/Intervals**

This session considers the understanding and use of confidence limits/intervals for:

(a) the mean of a normal distribution with both known and unknown variance,

(b) the difference between the means of two normal distributions with known variances. Also we consider approximate confidence limits, given large samples, for a probability or a proportion and interpreting all results in a practical context.

Each session of work will last 2-3 weeks.

At the beginning of the session you will receive a resource pack of study materials containing

- explanatory powerpoints with exercises and answers
- where appropriate, supporting geogebra or excel resources
- an additional powerpoint containing a selection of exam style questions (without solutions).

During the session you will have email access to the tutor and we hope to arrange a voluntary “drop-in” zoom meeting where you can discuss the content with other colleagues and/or the tutor.

At the end of the session there will be zoom meeting which, it is hoped, everyone will be able to attend. During this session, solutions to the powerpoint of exam style questions will be considered and there will be opportunities to discuss any difficulties that have occurred.