# Gwybodaeth Modiwlau

Module Identifier
MBM6010
Module Title
QUANTITATIVE METHODS (STATISTICS)
2009/2010
Co-ordinator
Semester
Semester 1
Other Staff

#### Course Delivery

Delivery Type Delivery length / details
Lecture 20 Hours. (20 x 1-hour lectures per week)
Practical 4 Hours. (4 computing practicals)
Other 8 Hours. (8 x 1-hours example classes, plus tutorials as required)

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment 2 Hours   (open book, in class test)  30%
Semester Exam 2 Hours   (written examination)  70%
Supplementary Exam 2 Hours   [If open book test passed (50% or more), mark is carried forward with weighting 30% and supplementary exam wil contribute 70%. If open book test failed, supplementary exam will be 100%.]  100%

### Learning Outcomes

On completion of this module, 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, including the construction of control charts, 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.

### Brief 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. The latter requires material on properties of standard probability 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 including applications to quality control.
The module will make substantial use of a statistical package for some of the calculations.

### Aims

To introduce students to 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.

### 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, 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. Applications. 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. Control charts and quality control.
7. Regression. Linear regression of y on x. Least squares estimates, the correlation coefficient, the fitted line, tests on slope and intercept, prediction.