00914 - Statistics

Learning outcomes

The course aims to provide the fundamental concepts and basic tools for statistical data analysis. By the end of the course, students will have acquired the knowledge and skills needed to apply the main statistical techniques for data exploration and description, as well as the basic principles of probability theory and statistical inference.

In particular, students will be able to:
(a) represent phenomena both graphically and through appropriate summary measures, and explore relationships between variables;
(b) perform probabilistic evaluations in basic applied contexts;
(c) carry out point and interval estimation, and test hypotheses in the case of random samples drawn from normal or binomial populations.

Course contents

DESCRIPTIVE STATISTICS

Introduction. Statistical surveys and stages of data collection. The data matrix.
Summarizing the distribution of a variable: absolute and relative frequencies, cumulative frequency distributions. Measures of central tendency and variability. Graphical representations.
Relationships between two variables: contingency tables; joint, marginal, and conditional distributions. Independence and measures of association. Linear dependence: covariance, correlation, and the simple linear regression model.

PROBABILITY CALCULUS

Introduction to probability. Random phenomena and uncertainty. Events and the sample space. Axioms of probability. Conditional probability and Bayes’ theorem.
Random variables: distribution, probability, and density functions. Expected value and variance. The Bernoulli and binomial distributions. The normal and standard normal distributions.
Independence of random variables. Sum of random variables and the Central Limit Theorem.

INFERENTIAL STATISTICS

Population model and parameters. Random sampling: estimators and their sampling distributions.
Point and interval estimation for the mean of a normal distribution and for a proportion.
Hypothesis testing: Type I and Type II errors, significance level. Statistical tests for the normal and binomial models.

Readings/Bibliography

S. Borra e A. Di Ciaccio (2008) Statistica. Metodologie per le Scienze Economiche e Sociali (IV ed.), McGraw-Hill.

P. Newbold, W.L. Carlson e B. Thorne (2021) Statistica (IX ed.), Pearson-Prentice Hall.

Teaching methods

Lectures, in-class exercises, homework assignments, and group projects.

Assessment methods

The exam is designed to assess the achievement of the course learning objectives, with particular reference to the knowledge and application of the fundamental tools of Statistics.

The exam aims to verify:

i) an in-depth understanding of the statistical tools presented during the lectures;
ii) the ability to apply these tools to data analysis;
iii) the ability to interpret the obtained results and use them to understand the studied phenomenon and support decision-making processes.

The exam consists of a written test (including exercises and open-ended questions), which is mandatory, and an oral examination at the discretion of the instructor.

Students may choose between the following options:

• Two midterm exams: in this case, the final grade will be the average of the two midterm grades. Each midterm lasts 45 minutes. The first midterm focuses on topics related to Descriptive Statistics, while the second assesses knowledge and skills in Probability and Statistical Inference.

• A comprehensive final exam: the duration of the written test is 90 minutes.

During the exams, students are allowed to use lecture notes, a formula sheet, and a calculator.

Additional important information:

• To take the exam, students must register through the Almaesami platform.

• The use of smartphones, smartwatches, or other personal electronic devices is not permitted during the exam.

• The exam can only be taken during the official exam sessions as scheduled in the academic calendar.

• Students must present a valid ID card or a university badge to participate in the exam.

Teaching tools

Course materials and other supporting resources are available on Virtuale. Practical demonstrations are provided using statistical software.

Office hours

See the website of Rosamarie Frieri