Statistics, First Course

Aim

The course is intended to give basic knowledge of the theory and methods of statistical inference, i.e. how to use observed data to draw conclusions about phenomena influenced by random factors. By the end of the course, the student should be able to:

• use an appropriate probability model to describe and analyse observed data and draw conclusions concerning interesting parameters;
• derive point estimators of parameters and analyse their properties;
• understand the principles of statistical inference based on confidence intervals and hypothesis testing;
• construct confidence intervals and test hypotheses using observed data, draw conclusions and describe the uncertainty;
• explore the nature of the relationships between two or several variables by using simple or multiple linear regression models and discuss the adequacy of the models;
• find probability models and statistical methods in applications from engineering, economy and science and evaluate the results;
• use appropriate statistical software for certain types of statistical analyses.

Content

Chi-square-, t-, F-distribution. Point estimation, properties of estimators, the method of maximum likelihood, the method of moments and the least squares method. Confidence intervals and tests of hypotheses for one or several samples especially for normal, binomial and Poisson distribution and certain cases when the central limit theorem can be applied. Chisquare tests. Random vectors, mean vectors and covariance matrices. The multivariate normal distribution.Multiple regression, estimation of parameters, confidence intervals, prediction, analysis of variance table, selection of regression model.Statistical software is used for regression analysis.