MATH10282 - 2011/2012

 

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, random sampling.  [1]
• Representing sample data – the histogram, boxplot, numerical summary measures. [2]
• Probability models for data.  [2]
• 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.  [2]
• Point estimation – the bias and variance of an estimator, choosing between competing estimators.  [2]
• The likelihood function and maximum likelihood estimators for discrete variables.  [2]
• 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. [3]
• Hypothesis testing – introductory ideas and concepts.  [2]
• 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.  [3]
• Calculation of the probability of rejecting the null for a given value of the population parameter.  [1]
• Tests based on two independent samples for differences between two Normal means, two non-Normal means, two population proportions.    [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 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.

Assessment

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

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Arrangements