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, so called 'stochastic' situations. 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 are introduced and applied to a variety of contexts.
The module will make substantial use of the MINITAB statistical package for some of the calcuations.

Learning outcomes
On completion of this course, a student should be able tod:

• 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 paid data.
• formulate, carry out and interpret tests of hypotheses in common business contexts.
• use the least squares method to estimate a linear relationship between two ro more variables, interpret the fitted model and use it for prediction.
• make use of a computer package to carry out simple data analyses and interpret the output.

Syllabus
1. Summarising Data. Types of data. Frequency tables, pie and barcharts; descriptive statistics, hostograms and stem and leaf plots. Comparing data sets. X-Y plots, correlation.
2. Probability. Elementary rules, symmetric situations, combinatorics, 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. Applictions. Central Limit Theorem, approximation of the Binomial and Poisson distributions bythe 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.

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