MAST4006 (Mathematical Methods 1), MAST4009 (Probability)
OverviewIntroduction to R and investigating data sets. Basic use of R (Input and manipulation of data). Graphical representations of data. Numerical summaries of data.
Sampling and sampling distributions. ?² distribution. t-distribution. F-distribution. Definition of sampling distribution. Standard error. Sampling distribution of sample mean (for arbitrary distributions) and sample variance (for normal distribution) .
Point estimation. Principles. Unbiased estimators. Bias, Likelihood estimation for samples of discrete r.v.s
Interval estimation. Concept. One-sided/two-sided confidence intervals. Examples for population mean, population variance (with normal data) and proportion.
Hypothesis testing. Concept. Type I and II errors, size, p-values and power function. One-sample test, two sample test and paired sample test. Examples for population mean and population variance for normal data. Testing hypotheses for a proportion with large n. Link between hypothesis test and confidence interval. Goodness-of-fit testing.
Association between variables. Product moment and rank correlation coefficients. Two-way contingency tables. ?² test of independence.
This module appears in:
Method of assessment
80% examination and 20% coursework.
J. Devore and R. Peck. Introductory Statistics. (West 1990)
F. Daly et al. Elements of Statistics. (The Open University 1995)
G.M. Clarke and D. Cooke. A Basic Course in Statistics. (5th edition. Arnold. 2004)
D.V. Lindley and W.F. Scott. New Cambridge Statistical Tables (2nd edition. C.U.P. 1995)
J. Verzani. Using R for Introductory Statistics (2nd edition, CRC Press, 2014)
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate knowledge of the underlying concepts and principles associated with statistics;
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts in the following areas, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material: graphical and numerical summaries of data using R, point estimation, including maximum likelihood estimation for discrete data, interval estimation, hypothesis testing, association between variables;
3 apply the underlying concepts and principles associated with introductory statistics in several well-defined contexts, showing an ability to evaluate the appropriateness of different approaches to solving problems in this area;
4 make appropriate use of the statistical computer package R.
The intended generic learning outcomes. On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as R, online resources (moodle), internet communication;
7 communicate technical and non-technical material competently.
8 demonstrate an increased level of skill in numeracy and computation;
9 give an oral presentation;
10 work in small groups.