MATH10282 - 2011/2012
- Title: Introduction to Statistics
- Unit code: MATH10282
- Credits: 10
- Prerequisites: A-Level Mathematics, MATH10141 Probability 1
- Co-requisite units: None
- School responsible: Mathematics
- Members of staff responsible:
The aims of this course unit are to help students
- develop a knowledge of basic statistical concepts and methodology which build on the ideas in probability studied in MATH10141;
- develop practical statistical skills.
Brief Description of the unit
The course gives a general introduction to statistics and is a prerequisite for all future statistics courses.
On successful completion of this course unit students will be able to
- understand introductory statistical ideas and methodology;
- use the statistical computing software R to analyse data.
Future topics requiring this course unit
The statistics content is required for MATH20802, Statistical Methods and MATH20812, Practical Statistics 1. The background in R is also very useful for MATH20812, Practical Statistics I.
- Populations and samples, random sampling. 
- Representing sample data – the histogram, boxplot, numerical summary measures. 
- Probability models for data. 
- Sampling distributions of sample statistics - the sample mean and its distribution under Normality, using the Central Limit Theorem, the sample proportion, the sample variance, the chi-squared distribution. 
- Point estimation – the bias and variance of an estimator, choosing between competing estimators. 
- The likelihood function and maximum likelihood estimators for discrete variables. 
- Confidence intervals. Single sample procedures for a Normal mean and variance, the population proportion. Two sample procedures for the difference between two Normal means and the difference between two population proportions. 
- Hypothesis testing – introductory ideas and concepts. 
- Tests based on a single sample – the Normal mean (variance known and unknown), the Normal variance, a non-Normal mean parameter, the Binomial probability parameter. Relationship between CI’s and hypothesis testing. 
- Calculation of the probability of rejecting the null for a given value of the population parameter. 
- Tests based on two independent samples for differences between two Normal means, two non-Normal means, two population proportions. 
- G M Clarke and D Cooke, A Basic Course in Statistics (Fourth Edition) Oxford University Press, 1998;
- Robert V Hogg, Introduction to Mathematical Statistics (Sixth Edition) Prentice Hall, 2005;
- Sheldon M Ross, Introduction to Probability and Statistics for Engineers and Scientists (Third edition) Elsevier Science, 2004;
- Michael J Crawley, Statistics: An Introduction Using R. John Wiley & Sons Ltd, 2007
Teaching and learning methods
Two lectures per week plus either an examples class or computing workshop. There will be 4 computing workshops and 7 examples classes. In addition, students are expected to do at least five hours private study each week on this course unit.
Two coursework assignments (20%) plus a two hour end of semester examination (80%).