	Department of Mathematics & Computer Science

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MA2201 Introductory Statistics

MA2201(=MC265) Introductory Statistics

Credits: 10

Convenor: Dr M.J. Phillips

Semester: 1 (weeks 7 to 12)

Prerequisites:	essential: MA1061(=MC160)
Assessment:	Coursework: 20%	One and a half hour examination: 80%

Lectures:	18	Problem Classes:	5
Tutorials:	none	Private Study:	52
Labs:	none	Seminars:	none
Project:	none	Other:	none
Surgeries:	none	Total:	75

Explanation of Pre-requisites

The module MA1061 provides the basic probabilistic ideas for an introductory course in statistical methods.

Course Description

Statistics and statistical statements are almost unavoidable in many areas modern science. This course introduces some of the central ideas of modern statistical reasoning, and presents a number of the more basic procedures of elementary applied statistics.

Aims

To introduce the main concepts of statistical inference; point and interval estimation, and hypothesis testing. The likelihood function and maximum likelihood estimate, key concepts in much modern statistical analysis, are also introduced.

Objectives

On completion of this module, students should:

$\bullet$: know what is meant by an estimate, an estimator, and a sampling distribution;
$\bullet$: understand what is meant by an unbiased estimator;
$\bullet$: know the mean and variance of the sampling distribution of the sample mean;
$\bullet$: know how to write down a likelihood function and find a maximum likelihood estimate for simple models;
$\bullet$: have an informal understanding of the process of hypothesis testing and the meaning of -values;
$\bullet$: know what is meant by a confidence interval and the relationship between confidence intervals and hypothesis tests;
$\bullet$: be able to apply a number of simple standard statistical procedures, recognise when these procedures are appropriate, and interpret the results of these procedures.

Transferable Skills

$\bullet$: An understanding of some basic statistical concepts including point and interval estimation, and hypothesis testing.
$\bullet$: The ability to implement and interpret the results of some simple statistical procedures, and recognise when such procedures are appropriate.

Syllabus

Basic graphical methods and descriptive statistics.

Different approaches to inference. Point estimation; mean squared errors, variance and bias. Estimates, estimators and sampling distributions. Standard unbiased estimators of a population mean and variance. Likelihood and the maximum likelihood estimator.

Hypothesis testing and confidence intervals. Inferences for the normal, binomial and Poisson distributions. Comparing two populations. Small sample results for normal populations; the -test. Paired and unpaired samples, the and $\chi^2$ distributions.

Simple examples of the $\chi^2$ goodness-of-fit test.

Reading list

Details of Assessment

The final assessment of this module will consist of 20% coursework and 80% from a one and a half hour examination during the January exam period. The 20% coursework contribution will be determined by students' solutions to coursework problems. The examination paper will contain 4 questions with full marks on the paper obtainable from 3 complete answers.