Course: 2023/2024

Introduction to Statistical Modeling

(16485)

Students will acquire knowledge and skills necessary to:
1. Define populations for a statistical study
2. Compute point estimators and confidence intervals for population parameters
3. Build Hypothesis about a distribution
4. Test hypothesis about the parameters of the chosen model
5. Evaluate how well does the model fit to reality
6. Understand the limitations of the methods that have been studied and the conditions under which they lead to wrong conclusions
7. Carry out the abovementioned analyses in statistical software
Students will be able to:
1. Develop their ability to think analytically
1. Become familiar with a statistical software
2. Establish a framework to solve problems
3. Develop their interactive skills
4. Enhance their critical thinking
5. Improve their learning skills and communication

Skills and learning outcomes

Description of contents: programme

1. Introduction to Statistical inference.
1.1. Population and sample
1.2. Random sampling
1.3. Fundamental sampling distributions
1.4. Point estimation of parameters
1.4.1. Definitions
1.4.2. Method of moments
1.4.3. Maximum likelihood estimation
2. Confidence intervals for a single sample
2.1. Introduction
2.2. CI on the mean
2.2.1. Normal population with known variance
2.2.2. Large sample
2.2.3. Normal population unknown variance
2.3. CI on the proportion
2.3.1. Large-sample
2.4. CI on the variance
2.4.1. Normal population
3. Test of hypotheses for a single sample
3.1. Introduction
3.2. Type I and Type II Errors
3.3. Power of a statistical test
3.4. P-value
3.5. HT on the mean
3.5.1. Normal population with known variance
3.5.2. Large sample
3.5.3. Normal population with unknown variance
3.6. HT on the proportion
3.6.1. Large sample
3.7. HT on the variance
3.7.1. Normal population
4. Statistical inference for two samples
4.1. Introduction
4.2. Difference in means
4.2.1. Normal populations with known variances
4.2.2. Large samples
4.2.3. Normal populations with unknown variances
4.2.4. Normal populations with unknown equal variances
4.2.5. Normal populations, paired observations.
4.3. Difference in proportions
4.3.1. Large samples
4.4. Ratio of the variances
4.4.1. Normal populations
5. Analysis of Variance
5.1. Introduction
5.2. One-way ANOVA
5.3. ANOVA table
5.4. Multiple comparisons
5.5. Two-way ANOVA.
6. Goodness of fit tests
6.1. Introduction
6.2. Chi-square tests
6.3. Kolmogorov-Smirnov test
6.4. Graphical tools

Learning activities and methodology

- Lectures: introducing the theoretical concepts and developments with examples, 2.2 ECTS
- Problem solving sessions: 2.2 ECTS
- Computer (practical) sessions: 0.6 ECTS -- 4 SESSIONS
- Evaluation sessions (continuous evaluation and final exam): 1 ECTS

Assessment System

- % end-of-term-examination 0
- % of continuous assessment (assigments, laboratory, practicals...) 100

Basic Bibliography

- MONTGOMERY, D.C., RUNGER, G.C.. Applied Statistics and Probability for Engineers. John Wiley & Sons. 2003
- Navidi, W.. Statistics for Engineers and Scientists. McGraw-Hill. 2006
- SONG, TT. . Fundamentals of Probability and Statistics for Engineers. John Wiley & Sons. 2004

Additional Bibliography

- GUTTMAN, L., WILKS, S.S., HUNTER, J.S. . Introductory Engineering Statistics. . Wiley. . 1992
- Newbold, P.. Statistics for Business and Economics.. Prentice-Hall.. 1995.
- PEÑA, D.. Regresión y Diseño de Experimentos.. Alianza Editorial.. 2002
- PEÑA, D. . Fundamentos de Estadística.. Alianza Editorial.. 2001

The course syllabus may change due academic events or other reasons.