Business Statistic II

Statistical inference deals with techniques that are highly useful in the economics-business field, as it allows as it allows for valid conclusions to be drawn about population behavior based on sample data. The basic objective of the subject is for the student to:
- Acquire knowledge and understanding of the concepts and methods of probability and statistical inference, as well as their application to the analysis of economic and business phenomena.
- Perform basic statistical analysis using computer tools.
- Be able to select and apply the most appropriate statistical techniques to the analysis of each phenomenon, as well as to interpret the results obtained.
- Initiate the analysis of empirical data related to economic and business reality (data collection, statistical analysis, model selection, interpretation and reliability of results, etc.) and the formal presentation of the work done.
- Develop skills in understanding, reasoning, criticism and oral and written expression, by using an appropriate statistical-economic vocabulary.

TOPIC 1 PROBABILITY
1.1 Theories of probability in statistics: classical, frequentist, subjective and axiomatic. Kolmogorov's Axioms
1.2 Conditional, joint and total probability. Theorems.
1.3 Bayes' theorem
1.4 Independence of events.

TOPIC 2 PROBABILITY DISTRIBUTIONS
2.1 Random variables: discrete and continuous.
2.2 Probability distributions of a random variable
2.3 Characteristics associated with random variables. Mean, variance, moments.
2.4 Generalization to the bivariate and multivariate case.

TOPIC 3 DISCRETE AND CONTINUOUS PROBABILITY MODELS
3.1 Binomial distribution.
3.2 Poisson distribution.
3.3 Univariate and bivariate Normal distribution.
3.4 Distributions derived from the Normal distribution: Chi-square, t-Student, F-Snedecor.

TOPIC 4 INTRODUCTION TO STATISTICAL INFERENCE
4.1 Statistical Inference: populations and random samples.
4.2 Statistics and estimators.
4.3 Distribution of sample mean, variance and proportion.

TOPIC 5 ESTIMATION
5.1 Estimation. Properties of point estimators
5.2 Methods of point estimation: method of moments and maximum likelihood.
5.3 Interval Estimation. Construction methods for confidence intervals. Confidence intervals in normal populations.

TOPIC 6 HYPOTHESIS TESTING
6.1 Basic concepts: types of hypotheses, critical region and acceptance region, types of errors, power of the test.
6.2 Methodology of hypothesis testing.
6.3 Common hypothesis tests.

BASIC

Fernández- Abascal, H., M. Guijarro, J.L. Rojo, J.A. Sanz. (1994): Cálculo de Probabilidades y Estadística. Ed. Ariel.
Lind, D.A.; Marchal, W.G. ; Wathen, S.A. (2015, 2012, 2008): Estadística Aplicada a los Negocios y a la Economía. Ed. McGrawHill.
Newbold, P. et al. (2008). Estadística para los Negocios y la Economía. Prentice-Hall.
Ruiz-Maya, L. (2004, 2002, 1999): Fundamentos de Inferencia Estadística. Ed. AC.

Esta materia contará con materiales elaborados por el profesorado, a disposición del alumnado en el CURSO VIRTUAL de la materia. http://www.usc.es/campusvirtual/

COMPLEMENTARY
Anderson, D. R.; Sweeney, D.J., Williams, T.A. (2001): Estadística para Administración y Economía. Vol.I. Thomson ed.
Berenson, M.L., Levine, D.M. (1996): Estadística Básica en Administración. Conceptos y Aplicaciones. Ed. Pearson Educación / Prentice Hall.
Canavos, G.C. (1997). Probabilidad y Estadística. Aplicaciones y Métodos. Ed. McGraw Hill.
Casas Sánchez, J.M. (1996): Inferencia Estadística para Economía y Administración de Empresas. Ed. Centro de Estudios Ramón Areces.
Durá Peiró, J.M., López Cuñat, J.M. (1989): Fundamentos de Estadística. Estadística descriptiva y Modelos Probabilísticos para la Inferencia. Ed. Ariel.
Freund, J.E., Miller, I., Miller, M. (2000): Estadística matemática con aplicaciones. Ed. Pearson Educación / Prentice Hall.
García Barbancho, A. (1992): Estadística Teórica Básica. Probabilidad y modelos probabilísticos. Ed. Ariel.
Kazmier, L.J. (2006): Estadística aplicada a administración y economía. Ed. MnGraw Hil.
Martín Pliego, F.J., L. Ruiz-Maya. (1998): Fundamentos de Probabilidad. Ed. AC. (2ª edición, 2006)
Levin, R.I., Rubin, D.S. (1996): Estadística para administradores. Ed. Pearson Educación / Prentice Hall.
Novales Cinca, A. (1998): Estadística y Econometría. Ed. McGraw Hill.
Peña, D.; Romo, j. (1997): Introducción a la Estadística para las Ciencias Sociales. Ed. McGrawHill.
Ruiz-Maya, L., F.J. Martín Pliego. (1999): Fundamentos de Inferencia Estadística. Ed. AC. (2ª ed. 2000; 3ª ed.2005).
Sarabia Alegria, J.M. (2000): Curso práctico de estadística. Ed. Civitas.
Spiegel, M.R.; Schiller, J. ; Alu Srinivasan, R. (2010): Probabilidad y Estadística. Ed. McGraw-Hill.
Triola, M.F. (2004): Estadística. Ed. Pearson Educación.
Webster A.L. (1996): Estadística aplicada a la empresa y a la economía. Ed. Irwin.

EXERCICES BOOKS
Baró Llinás, J. (1987): Cálculo de probabilidades. Ed. Parramón.
Baró Llinás, J. (1989): Inferencia estadística. Ed. Parramón.
Fernández- Abascal, H., M. Guijarro, J.L. Rojo e J.A. Sanz. (1995): Ejercicios de Cálculo de Probabilidades. Ed. Ariel.
Martín Pliego, F.J., Montero Lorenzo, J.M. e Ruiz-Maya L. (1998): Problemas de probabilidad. Ed. AC.
Martín Pliego, F.J., Montero Lorenzo, J.M. e Ruiz-Maya L. (2000): Problemas de inferencia estadística. Ed. AC.

BASIC AND GENERAL
CB1 - To demonstrate knowledge and understanding in a field of study that builds upon general secondary education, and is tipically at a level of supported by advanced textbooks, including some cutting-edge of the field.
CB2 - To apply knowledge to their work or vocation in a professional manner and possess the skills typically demonstrated through the development and defense of arguments and problem-solving within their field of study.
CB3 - To gather and interpret relevant data (tipically within their field of study) to make judgments that include reflection on relevant social, scientific, or ethical issues.
CB4 - To communicate information, ideas, problems and solutions to both specialized and non-specialized audience.
CB5 - To develop the learning skills necessary for further studies with a high degree of autonomy.
CG2 - To be able to develop and defend arguments on economic issues at a general level, as well as solve problems related to these issues, using their knowledge of the business reality, theories, models, and scientific methods involved.
CG3 - To be able to identify, gather and interpret relevant data on issues related to the business environment, incorporating relevant considerations of their social, scientific, or ethical dimensions into the formulation of judgements and proposals.

TRANSVERSAL
CT1 - -Analysis and synthesis.
CT4 - -Information management.
CT5 - -Information technology knowledge related to the field of study.
CT6 - -Problem-solving.
CT7 - -Decision-making.
CT8 - -Critical reasoning.
CT9 - -Autonomy in learning.
CT13 - -Ethical awareness.
CT16 - -Sensitivity to social and environmental problems.
CT22 - -Development of quality.

SPECIFIC
C2 - Basic elements of descriptive statistics, probability, and statistical inference
D6 - Identify relevant economic information sources and their content.
D8 - Derive relevant information from data that may not be recognized by non-professionals.
D10 - Apply professional criteria based on the use of technical instruments to analyze problems.

The course incorporates a combination of expository and interactive teaching methods, supplemented by individual and/or small group tutorials.

Additionally, a virtual classroom will be available on the USC platform, providing students with access to classroom presentations and supporting materials for the course and subject preparation.

EXPOSITORY CLASSES
The expository classes aim to introduce and explain the fundamental aspects of each topic, offering further information essential for fostering autonomous learning.

INTERACTIVE CLASSES AND PRACTICES WITH COMPUTER
In interactive classes, students are expected to learn how to apply statistical techniques to the analysis of economic and business realities. They will learn to differentiate which techniques to employ in specific cases, how to apply them effectively, and how to draw meaningful conclusions from the analysis. To facilitate this learning process, practical problems and activities will be provided for students to solve individually or in small groups. These interactive practices will be complemented by computer-based activities that aim to enhance students' skills in using spreadsheets or other statistical software packages for data analysis.

SCHEDULED TASKS AND TESTS
Continuous assessment activities, built upon computer-based practices, may involve the statistical analysis of empirical phenomena using real databases throughout the semester, leveraging computer tools. The purpose of these tasks is to facilitate students in acquiring skills related to conducting statistical analyses of empirical reality. Students will learn how to select and apply appropriate statistical techniques to analyze each phenomenon, utilize computer tools for data analysis, accurately interpret the results obtained, and effectively present and defend their work using discipline-specific vocabulary. Additionally, individual or group assessments may be conducted to evaluate students' comprehension and mastery of the content covered.

INDIVIDUAL OR SMALL GROUP TUTORING
Tutorials provide students with ongoing guidance from faculty members to support them in completing the assigned activities. Many of these activities are intended to be carried out autonomously by the students. Tutorials also offer an opportunity for students to seek clarification and address any doubts they may have regarding the subject matter.

The student has the option to choose between a continuous assessment system or a single assessment system at the beginning of the semester. The preferred evaluation system is continuous assessment, which utilizes instruments to measure the ongoing learning of statistical concepts and methodologies covered in the subject, as well as their application to empirical reality. It is primarily based on tasks in which students demonstrate their level of acquired knowledge. Anyone who takes any test or completes any task will automatically be included in the continuous assessment system.

1st OPPORTUNITY

A) Continuous Evaluation System. Assessment instruments and their weight in the final grade:
- Exam: 70% of the total grade (7 points).
- Continuous assessment activities: 30% of the total grade (3 points).

Continuous assessment activities will primarily focus on practical exercises and board or computer-based tests, as well as discussions and problem-solving activities in groups.

To pass the subject, it is necessary to obtain a total score (exam + continuous evaluation) of 5 or higher out of 10.

B) Single Assessment System. Students who choose this system will be exclusively graded through the final exam of the subject, which will be scored out of 10 points.

2nd OPPORTUNITY

In the evaluation of the 2nd Opportunity, students who have chosen the continuous evaluation system can either continue with it or switch to the single assessment system. At the time of the exam, the student will indicate whether they wish to remain in the continuous evaluation system (where the exam will be scored out of 7 points) or opt for the single assessment system (where the exam will be scored out of 10 points). To obtain the final grade for the subject, in the first case, the continuous assessment score obtained throughout the course will be maintained and added to the exam score. In the second case, the final grade of the subject will be the same as the grade obtained in the exam. Students will not have the possibility to recover tasks, activities, or previous tests that were pending completion for students linked to continuous evaluation.

To take the exams, it will be necessary to present an official identification document (DNI, Passport ...)

Attendance at activities will be governed by the regulations of the USC. Evaluation in cases of class attendance waiver will be based on the final test scored with the maximum possible grade.

According to the current Permanence regulations at USC for Bachelor's and Master's studies (article 5.2), attendance and/or participation in any activities subject to evaluation will result in a final grade different from “Absent”.

In cases of fraudulent performance of exercises or tests, the provisions of the "Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións" will apply.

Competency Assessment

Continuous Evaluation: CB2, CB3, CB4, CB5, CG2, CG3, CT1, CT4, CT5, CT6, CT7, CT8, CT9, CT13, CT16, CT22, D6, D8, D10.

Exam Assessment: CB1, CB2, CB5, CG2, CT1, CT6, CT7, CT8, C2, D8, D10.

Following the degree program's guidelines, the course includes 60 hours of face-to-face classroom work and 90 hours of personal student work.

-To have successfully completed the subjects of Business Statistics I and Business Mathematics I and II.
-Work on the subject daily in order to make the most of the classes, both for understanding the content and for asking questions in the classroom (it is beneficial for the whole group) or during tutorials.
-Do not neglect any assigned work or tasks.
-Do not abandon the subject even if the partial assessments are not positive, as long as you are willing to continue working.

Language: Galician
Use of Virtual Classroom: Yes
Interactive Teaching: Computer Lab, Whiteboard Classroom
Software: R, SPSS, Excel, ...