MA1501: Statistical Inference
School | Cardiff School of Mathematics |
Department Code | MATHS |
Module Code | MA1501 |
External Subject Code | 100406 |
Number of Credits | 10 |
Level | L4 |
Language of Delivery | English |
Module Leader | Professor Jonathan Gillard |
Semester | Spring Semester |
Academic Year | 2018/9 |
Outline Description of Module
The role of statistics in the modern world is ever increasing and applications can be found in a wide variety of areas including science, industry, government and commerce making a basic understanding of statistics an essential skill. This is a lecture based module given at an introductory level on statistical inference to develop an understanding of the basic principles of mathematical statistics, used in situations where the full picture of a problem (population) is unknown and must be inferred from collected data (random sample).
This module will be accessible to those who have knowledge of A-level Pure Mathematics and an Introduction to Probability Theory. It will prepare students for all modules with statistics and probability content in future years of the degree scheme.
Free Standing Module Requirements: A pass in A-Level Mathematics of at least Grade A
Precursor Module: MA1500 Introduction to Probability Theory
On completion of the module a student should be able to
- Create sampling distributions for various sample statistics.
- Determine confidence intervals for the sample mean, the difference between sample means, the variance and the ratio of two sample variances for a given large or small sample.
- Understand the concept of hypothesis testing, used to help scientists choose between two possible alternatives, and be aware of different types of errors that occur.
- Be able to perform a goodness of fit test to check the validity of an assumption that a distribution has a particular form and also be able to test for independence when looking at data which is split into different categories.
- To fit a straight line to experimental data.
How the module will be delivered
27 fifty-minute lectures
5 fifty-minute tutorial classes
Some handouts will be provided in hard copy or via Learning Central, but students will be expected to take notes of lectures.
Students are also expected to undertake at least 50 hours private study including preparation of worked solutions for tutorial classes.
Skills that will be practised and developed
Be able to undertake a simple statistical analysis on random data sets and have an appreciation of the problems involved in interpreting results. An essential skill in almost every career.
How the module will be assessed
Formative assessment is carried out by means of regular tutorial exercises. Feedback to students on their solutions and their progress towards learning outcomes is provided during tutorial classes.
The summative assessment is the written examination at the end of the module. This gives students the opportunity to demonstrate their overall achievement of learning outcomes. It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.
The examination paper has two sections of equal weight. Section A contains a number of compulsory questions of variable length but normally short. Section B has a choice of two from three equally weighted questions.
Assessment Breakdown
Type | % | Title | Duration(hrs) |
---|---|---|---|
Exam - Spring Semester | 100 | Statistical Inference | 2 |
Syllabus content
- Sampling Distributions
- To be able to create sampling distributions of the sample mean, variance, median, maximum, etc., for small samples drawn with replacement from a population.
- Specific Distributional Results
- Students should be able to state the Central Limit Theorem, and derive and use properties of some important distributions.
- Confidence Intervals
- Students should be able to derive and use confidence intervals for means (and their differences), variances (and their ratios).
- Hypothesis Testing
- Students should be able to understand the concept of hypothesis testing and, in particular, the meaning of Type I error, Type II error and the p-value of a test. Significance testing should be restricted to the binomial, Poisson and normal distributions. This will include the study of one-way ANOVA.
- Chi-Square Tests
- Students should be able to perform a Chi-square goodness of fit test and be able to test for independence using contingency tables.
- Simple Linear Regression
- Students should be able to fit a straight line to experimental data, and perform inferences on this fit.
Essential Reading and Resource List
Not applicable.
Background Reading and Resource List
Grimmett, G. and Stirzaker, D. 2001. Probability and random processes. 3rd ed. OUP
Hogg, R. and Tanis, E. 2014. Probability and statistical inference. 9th ed. Pearson.