STATISTICS - 2

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 the following.
First period:
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;
3. Bivariate discrete random variables, covariance and correlation; some relevant properties of multivariate random variables;
Second period.
4. Descriptive statistics: data collection and classification; frequency distributions; the main statistica indeces; graphical tools.
5. Sequencies of random variables, laws of large numbers, the central limit theorem.
6. Statistical inference: parametric statistical model and sampling; point and interval estimation; hypothesis 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, 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, and 7.4 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 examination consists of a 90-minute written test comprising multiple-choice and open-ended questions. Sample examination papers are available on the course Moodle page. The maximum score is 30/30.
The use of notes or textbooks is not permitted; only a pocket calculator and statistical tables may be used.
Students who achieve a score of at least 18/30 may request an oral examination. The instructor reserves the right, in any case, to require a student to take an oral examination. For scores of 27/30 or higher, the oral examination is mandatory.
Failure to take the oral examination, when mandatory or required by the instructor, or failure to pass it results in failure of the examination, irrespective of the score obtained in the written test.

written

The instructor is responsible for ensuring the authenticity and originality of all examinations and coursework. In cases of suspected academic misconduct, an additional on-site assessment may be required during the exams, which may differ from the standard format.

Incorrect or missing answers on the written test do not result in any penalty. The grade is based on the evaluation of the following elements, demonstrated by the student in both the written and oral exams:
a) understanding of the fundamental concepts of the subject;
b) argumentative skills;
c) correctness in the use of statistical-probabilistic language (including formal language).
The grading scale follows the following correspondence between assessments and scores:
barely sufficient, in the presence of several gaps: rades 18-20;
- fully sufficient: grades 21-23;
- good: 24-26;
- excellent: 27-30;
- outstanding: 30 cum laude.

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