Specific Objectives 1. Understand the fundamentals of statistical inference, including the concepts of simple random sampling, population parameters, sample statistics, and the associated sampling distributions. 2. Analyze the key properties of estimators, such as unbiasedness, efficiency, consistency, invariance, robustness, and sufficiency. 3. Apply classical parameter estimation methods, including the method of moments and maximum likelihood estimation. 4. Construct confidence intervals for population parameters, using the pivotal quantity method for both single-sample and two-sample scenarios. 5. Interpret and apply parametric hypothesis testing, understanding the concepts of null and alternative hypotheses, Type I and Type II errors, statistical power, testing methodology, and p-values. Cross-Curricular Objectives: 1. Develop critical and analytical thinking skills through the interpretation of statistical results in real-world contexts, fostering evidence-based decision-making. 2. Strengthen proficiency in the precise use of mathematical and statistical language, promoting conceptual clarity and logical reasoning. 3. Encourage both independent and collaborative work skills, through problem-solving, report writing, and group discussions of statistical results. 4. Promote the use of technological tools and statistical software to support data analysis and processing, integrating theoretical knowledge with practical application. 5. Foster an ethical and responsible approach to data handling and interpretation, recognizing the impact of statistical findings across various fields of knowledge and society.

1. Introduction to statistical inference. 1.1 Simple random sample, parameters and sample statistics. 1.2 Distributions in sampling for a population. 1.3 Mean and variance of the sample mean and the sample variance and distribution in the case of normal distribution. 2. Properties of the estimators. 2.1 Unbiasedness, efficiency, consistency, invariance and robustness. 2.2 Sufficiency. Factorization theorem. 3. Parameter estimation methods. 3.1 Method of Moments. 3.2 Estimation by maximum likelihood. 4. Confidence intervals. 4.1 Definition of confidence interval. 4.2 Pivotal quantity method to obtain confidence intervals. 4.3 Confidence intervals for a sample. 4.4 Confidence intervals for two samples. 5. Introduction to parametric hypothesis testing 5.1 Definition of statistical hypothesis and hypothesis testing. 5.2 Null and alternative hypotheses. 5.3 Type I and type II errors. 5.4 Power of a contrast. 5.5 Methodology of a hypothesis test. 5.6 Definition and interpretation of the p-value. 5.7 Hypothesis tests for one and two samples.

Theory (3 ECTS): Theoretical classes focused on the presentation and discussion of the core contents of the course, supported by teaching materials available on Aula Global. Active student participation will be encouraged through questions, illustrative examples, and connections to real-world applications of statistical inference. Practice (3 ECTS): Practical sessions dedicated to problem-solving and applied exercises related to the theoretical content. These include computational labs using statistical software for the analysis of real and simulated data, promoting hands-on and independent learning. Additionally, group projects will be carried out to apply acquired knowledge to specific scenarios, fostering teamwork and communication skills.