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, capitoli 1-26.

The final exam is a 90-minute written test consisting of both multiple-choice and open-ended questions.
Examples of written tests are available in the dedicated course area on the university's Moodle e-learning platform. The maximum score for this test is 30/30.
During the exam, the use of notes, textbooks, or other aids is not permitted, with the exception of a pocket calculator and statistical tables.
All students who pass the written test (by obtaining a score of no less than 18/30) have the option to request an oral integration. For students who achieve a score of no less than 27/30 on the written exam, the oral exam is mandatory.
The exam aims to assess: i) the understanding of the fundamental concepts; ii) the ability to solve simple exercises; iii) the capacity for logical reasoning and the appropriate use of statistical and probabilistic terminology.

written

The final grade is based on both written and oral exam performance, evaluating:
a) understanding of key concepts;
b) reasoning and argumentation skills:
c) correct use of statistical-probabilistic language (including formal notation).
Grading Scale:
- 18–20: Barely sufficient, with several conceptual gaps;
- 21–23: Sufficient, meets minimum expectations;
- 24–26: Good understanding and application;
- 27–30: Very good to excellent performance;
Honors (lode) will be awarded only to those who exhibit exceptional judgment and an in-depth understanding of the topics covered.

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