Statistics for Engineers, 7.5 Credits

Contents

Module 1 (3 ECTS): Basic Probability and Statistical Theory
The notions probability, discrete and continuous random variable, probability function, probability density function, cumulative distribution function, expected value, variance, standard deviation, covariance and correlation, are defined. Furthermore, the most common probability distributions for technical applications are treated, with special emphasis on the normal distribution, distributions for linear combinations of normally and non-normally random variables (in the latter case applying the central limit theorem), and approximations of expected values and variances for non-linear functions of random variables. The notions point estimate, unbiasedness, efficiency, hypothesis, significance level, power, type I and II errors, rejection region, p value and confidence level, are defined. The t-, Chi2-, and F-distributions are applied for hypothesis testing and interval estimation for one and two samples. Furthermore the basics of stochastic simulation, bootstrap and permutation tests, are treated. Finally the analysis of contingency tables, basic analysis of variance, and simple and multiple linear regression analysis, are covered.

Module 2 (4,5 hp): Applications using Statistical Software
The theory from Module 1 is applied on problems from areas the students might run into after their education. The data analysis is mainly done with the support of suitable statistical software, focusing mainly on presenting problems and solutions both in oral and written form.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• account for the basic notions and laws from probability theory, that are included in the course
• account for the basic notions from inference theory, that are included in the course

Skills

• summarize the results from a statistical study in written and oral form
• apply probability-, probability density- and cumulative distribution functions in order to calculate probabilities, expected values, variances, and standard deviations for random variables
• apply the central limit theorem for probability calculations for linear combinations of random variables.
• set up appropriate null- and alternative hypotheses for conducting statistical tests
• analyze data with the statistical methods in the course, with as well as without the assistance of statistical software

Judgement and Approach

• evaluate the results from a statistical study and draw relevant conclusions
• through judgements, and with account to relevant scientific and ethic aspects, decide what statistical methods are suitable for the analysis of existing data

Required Knowledge

The course requires 15 ECTS in Mathematics including derivatives and integrals, or corresponding.

Form of instruction

The teaching consists mainly of lectures and problem solving sessions. The problem solving sessions mainly consist of supervision and demonstrations using suitable statistical software.

Examination modes

Modules 1 is assessed through written examination. Module 2 is assessed through oral and written presentations of home assignments. For Modules 1 and 2, one of the following judgements are awarded: Failed (U), Passed (3), Passed with merit (4), Passed with distinction (5). For the course, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). To pass the whole course, all modules must have been passed. The grade is decided from a weighted mean of the scores on the exam and the home assignments, where 60% weight is on the exam and 40% on the home assignments, and is set when all compulsory modules have been assessed.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Examiners may decide to deviate from the modes of assessment in the course syllabus. Individual adaption of modes of assessment must give due consideration to the student's needs. The adaption of modes of assessment must remain within the framework of the intended learning outcomes in the course syllabus. Students who require an adapted examination must submit a request to the department holding the course no later than 10 days before the examination. The examiner decides on the adaption of the examination, after which the student will be notified.

Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå University, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications.

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics.

The course can be included as a course in the main subject Mathematics on the basic level.

In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.