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Department of Mathematics



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MA2201 Introductory Statistics

MA2201 Introductory Statistics

Credits: 10 Convenor: Dr. M.J. Phillips Semester: 1 (weeks 7 to 12)
Prerequisites: essential: MA1061
Assessment: Examination and coursework: 80:20% Examination: 0%
Lectures: 18 Problem Classes: 5
Tutorials: none Private Study: 52
Labs: none Seminars: none
Project: none Other: none
Surgeries: none Total: 75

Subject Knowledge

Aims

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

Learning Outcomes

Students should know what is meant by an estimate, an estimator, and a sampling distribution; understand what is meant by an unbiased estimator; know the mean and variance of the sampling distribution of the sample mean; know how to write down a likelihood function and find a maximum likelihood estimate for simple models. Students should have an informal understanding of the process of hypothesis testing and the meaning of $P$-values and know what is meant by a confidence interval and the relationship between confidence intervals and hypothesis tests.

Methods

Class sessions with some handouts.

Assessment

Marked problem sheets and examination.

Subject Skills

Aims

To provide students with the ability to calculate estimates and make inferences about the parameters of some simple statistical models.

Learning Outcomes

Students will have an understanding of some basic statistical concepts including point and interval estimation, and hypothesis testing. They will also have the ability to implement and interpret the results of some simple statistical procedures, and recognise when such procedures are appropriate.

Methods

Class sessions.

Assessment

Marked problem sheets and examination.

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.

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 $t$-test. Paired and unpaired samples, the $F$ and $\chi^2$ distributions.

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

Reading list

Recommended:

W. Mendenhall, R. L. Scheaffer and D. D. Wackerly, Mathematical Statistics with Applications, 6th edition, Duxbury Press, 2002.


Resources

Problem sheets, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA2251 Linear Regression Models Up: ModuleGuide03-04 Previous: MA2161 Algebra II

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Last updated: 2004-02-21
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