STATISTICS - 1

This course is part of the “core educational activities” of the degrees in “Economics and Business” and “Economics of Tourism”. It is a single 12 credit compulsory course taught in two terms (one semester). It aims at introducing the statistical inference principles and tools most commonly used in economic empirical analysis. Estimation and hypothesis testing are illustrated for both the main parametric models and some relevant nonparametric applications (goodness of fit, independence, homogeneity). A relevant part of the course concerns those probability theory topics that are propedeutical to inferential techniques.

The course aims at providing an adequate knowledge of the main probabilistic and inferential tools used in the empirically based analysis and interpretation of economic phenomena.

The exam of Mathematics (ET0045) is a prerequisite for the exam of Statistics. Therefore, the topics covered by both Mathematics (ET0045) and Mathematics: prerequisites (ET0101) courses are assumed to be as known.

The full 12 credit course programme is:

1. Elementary probability calculus: definitions, axioms and property of the probability measure; conditional probability and stochastic independence; Bayes theorem.
2. Random variables: discrete and continuous variables; expected value and moments; quantiles; transformations of random variables; some relevant models of univariate random variables; bivariate discrete random variables, covariance and correlation; some relevant properties of multivariate random variables; sequencies of random variables, laws of large numbers, the central limit theorem.
3. Descriptive statistics: data collection and classification; frequency distributions; the main statistica indeces; graphical tools.
4. Statistical inference: parametric statistical model and sampling; point and interval estimation; hypothesis testing; goodness of fit, independence and homogeneity testing.

Textbook:
Boella M., Probabilità e Statistica per ingegneria e scienze. Pearson, II ed. 2020. Chapter 1 (escluso paragrafo 1.8); Chapter 2 (sections 2.5.3 , 2.6.2, 2.6.6. and 2.8 can be omitted); Chapter. 3 (sections 3.1.3, 3.1.4, 3.5 can be omitted); Chapter 4 (sections 4.4, 4.6, 4.7.2 and 4.8 can be omitted); Chapter. 5 (section 5.3.3 can be omitted); Chapter 6 (sections 6.2, 6.3.3 and 6.4.2 can be omitted); Chapter 7 (sections 7.3.3, 7.4.4, 7.4.5 and 7.4.6 can be omitted); Appendix A, Appendix B (section B.4.2 can be omitted), Appendix C, Appendix D (sections from D.6 to D.13 can be omitted)

Further readings (exercises and applications):
Monti, A. C.: Statistica. Esercizi svolti. Pearson, 2024.
Pauli F., Trevisani M., Torelli N., Statistica: esercizi ed esempi, Pearson, 2008

The final assessment consists of a written test composed by single choice questions, exercises and theoretical: multiple choice questions aim to verify the calculation ability and the understanding of the fundamental concepts of the discipline; the exercises and open questions are intended to test the students' analytical and communication skills. Incorrect or missing answers do not give rise to any penalty. As regards the grading (how the grades will be assigned), regardless of the attending or non-attending mode:
A. scores in the 18-22 range will be awarded in case of:
- sufficient applied skills in relation to the programme;
- limited ability to manage and/or interpret probabilistic and statistical techniques;
- sufficient communication skills, especially in relation to the use of discipline-specific language;
B. scores in the 23-26 range will be awarded in the presence of:
- fair applied skills in relation to the programme;
- fair ability to manage and/or interpret probabilistic and statistical techniques;
- fair communication skills, especially in relation to the use of discipline-specific language;
C. scores in the 27-30 range will be awarded in the presence of:
- good or very good knowledge and ability to understand applied in relation to the programme;
- good or very good ability to manage and/or interpret probabilistic and statistical techniques;
- good or very good communication skills, especially in relation to the use of discipline-specific language;
D. the distincion of honors will be awarded in the presence of knowledge and ability to understand applied in reference to
program, judgment and communication skills, excellent.
Examples of multiple choice questions and exercises are available on Ca' Foscari Moodle elearning platform.
The exam is closed-notes and closed-book. Students are allowed to use a pocket calculator and two sides of an A4-sheet prepared by them at home.

The course is taught through presentation style lectures and classroom practicals integrated by the individual student activities. Students are supported by the indicated textbook and by the resources made available on Moodle platform.

Students are invited to enrol to the course at moodle.unive.it

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