Module Identifier MBM6010 Module Title QUANTITATIVE METHODS (STATISTICS) Academic Year 2001/2002 Co-ordinator Dr J Lane Semester Semester 1 Course delivery Lecture 2 per week Practical 4 Hours Computing Other 4 Hours Example Classes Assessment In-course assessment 2 Hours 30% Exam 2 Hours 70%

#### General description

The first part of the course deals with the dual but distinct problems of summarising and interpreting data and providing mathematical models for situations where there is inherent uncertainty. This requires material on properties of standard distributions. The concepts and rules are generously illustrated with examples from business or administrative contexts. The remaining part of the course is concerned with statistical inference. Here the basic ideas and elements are introduced and applied to a variety of contexts.
The module will make substantial use of the MINITAB statistical package for some of the calculations.

#### Aims

• to ground students in basic methods for summarising and interpreting data.
• to provide an understanding of, and working facility in, probability and statistical inference.
• to illustrate the uses of probability and statistics in solving business problems.

#### Learning outcomes

On completion of this course, a student should be able to
• identify common types of data; summarise and interpret them in business contexts.
• calculate probabilities and conditional probabilities in a variety of situations.
• select an appropriate probability distribution for common types of data; find relevant probabilities using tables, calculator or computer package.
• calculate the mean, variance and standard deviation of multiples and sums of independent random variables.
• calculate confidence intervals for single random samples and paired data.
• formulate, carry out and interpret tests of hypotheses in common business contexts.
• use a computer package to carry out simple data analyses and interpret the output.
• use a computer package to estimate a linear relationship between two or more variables, interpret the fitted model and use it for prediction.

#### Content

1. Summarising Data. Types of data. Frequency tables, pie and barcharts; descriptive statistics, histograms, stem and leaf, box and whisker plots. Comparing data sets. X-Y scatter plots, correlation.
2. Probability. Elementary rules, equally likely events, sampling with and without replacement. Applications.
3. Conditional Probability and Tree Diagrams. The chain rule, Bayes Rule. Applications. Expected value; decision making.
4. Probability Distributions. Binomial and Poisson, applications in modelling, 'rare event' model for the Poisson. Mean, variance and standard deviation, basic properties. Normal distribution, density function, use of Statistical Tables. Applications including Quality Control. Central Limit Theorem, approximation of the Binomial and Poisson distributions by the Normal distribution.
5. Confidence intervals. Single Normal random sample, distribution of the sample mean, confidence levels, confidence interval for the mean, with variance both known and unknown. Matched pairs. Large sample interval for the Binomial and the Poisson.
6. Hypothesis Testing. Examples for Normal, Binomial and Poisson data. Simple and composite hypotheses, critical (rejection) region, type I and II errors, P-value, significance level, power function, formulation of problems.
7. Regression. Linear regression of y on x. Least squares estimates, the correlation coefficient, the fitted line, tests on slope and intercept, prediction.
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