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

• 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.

You will be guided through learning activities appropriate to your module, which may include:

• Weekly face to face classes (e.g. labs, lectures, exercise classes)
• Electronic resources to support the learning (e.g. videos, exercise sheets, lecture notes, quizzes)

Students are also expected to undertake at least 50 hours of self-guided study throughout the duration of the module, including preparation of formative assessments.

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.

• 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.