LEARNING OUTCOMES

The main aim of the course is to provide students with the fundamental tools of descriptive and inferential statistical analysis. The first part - Elements of descriptive statistics - relates to the fundamental concepts of univariate and bivariate descriptive statistics and is essential for any subsequent study. The second part - Introduction to probability theory - is designed to present the basic ideas needed for the study of statistical inference. The third part - Introduction to statistical inference - addresses the fundamental issues of sampling and inference, with particular regard to the theory of estimation and hypothesis testing.

AIMS AND LEARNING OUTCOMES

Knowledge and understanding: Students will know the main tools used to summarize the information and for the generalization of the information observed through sample surveys. 

Ability to apply knowledge and understanding: Students will be able to reorganize data in univariate and bivariate frequency tables providing adequate graphical representations; carry out basic descriptive analyses for univariate phenomena; analyze the relationships between two or more phenomena with particular emphasis on association and linear regression analysis. They will also be able to apply some statistical inference tools to solve simple problems. 

Making judgements: Students must be able to use the acquired knowledge both on a theoretical and operational level with autonomous assessment skills, in various applicative contexts. 

Communication skills: Students will acquire the technical language typical of the discipline to communicate clearly and without ambiguity with both statisticians and non-statisticians. 

Learning skills: Students will develop adequate learning skills that allow them to continue to study the subject independently. 

Connections of the course with other courses in the programme: The topics introduced in this course will allow the students to properly understand numerical data within other disciplines and will put the bases to study and analyze quantitative methods in other quantitative courses. 

PREREQUISITES

The course requires knowledge of the basic skills of a course of General Mathematics for Business and/or Economics. 

TEACHING METHODS

Traditional lessons and exercises and through AulaWeb. Since the training objectives concern both theoretical and applicative skills, there will be both lessons focused on the methodological aspects of statistics and lessons based on exercises in which numerical problems are faced and examples of simple analyzes on real data are discussed. 

Due to the Covid19 pandemic, students will be informed via email and AulaWeb messages on the actual method of the lessons (in person or remotely). 

SYLLABUS/CONTENT

Part I: Elements of descriptive statistics

1. Introduction to data collection
2. Distribution of a variable and its representation: Frequency distributions and diagrams
3. Location indices: means, median, mode, percentiles
4. Scale indices
5. Measures of  concentration
6. Association measures for two variables
7. Statistical independence
8. Association between qualitative variables.
9. Correlation between quantitative variables
10. Simple linear regression

Part II: Probability

1. Events and events sigma-field
2. Kolmogorov axioms
3. Conditional probability and independence
4. Bayes theorem
5. Discrete and continuous random variables:
   1. Bernoulli and Binomial r.v.
   2. Poisson r.v.
   3. Normal r.v.
6. The Central Limit Theorem

Part III: Introduction to statistical inference

1. Sampling and sampling distributions
2. Point estimation
3. Estimators and their properties
4. Interval estimation
5. Confidence interval for a mean (variance unknown)
6. Confidence interval for a proportion
7. Theory of statistical
8. Test for a mean, test for a proportion.
9. Comparison of two means.

RECOMMENDED READING/BIBLIOGRAPHY

Foreign students are asked to contact the teachers to agree on the text book in English language.