MATH10282 - 2010/2011

 

Specification

Aims

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.

Learning Outcomes

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.

Syllabus

• Populations and samples, sample statistics, graphical summaries, probability models for data;  [4]
• Point estimators and their sampling distributions; How good are sample statistics as estimators of population parameters?  [2]
• The likelihood function and maximum likelihood estimators for discrete variables; [2]
• Confidence intervals; [1]
• Hypothesis testing – introductory ideas and concepts;  [2]
• Tests based on a single sample – the Normal mean (variance known), the Binomial probability parameter;  Relationship between CI’s and hypothesis testing;  [2]
• Calculation of the probability of rejecting the null for a given value of the mean;  [2]
• Chi-square distribution  - confidence intervals and tests on the variance of a Normal distribution, goodness-of-fit tests;  [1]
• t-distribution  - confidence intervals and tests on Normal mean with variance unknown;  [1]
• Tests based on two independent samples;   [3]
• One-way ANOVA – an introduction.  [2]

Textbooks

• 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 5 computing workshops and 6 examples classes. In addition, students are expected to do at least five hours private study each week on this course unit.

Assessment

Two coursework computing assignments (20%) plus a two hour end of semester examination (80%)

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Arrangements