Primary Reference (English)
📖 Newbold, P., Carlson, W. & Thorne, B. (2012) — Statistics for Business and Economics. 8th Edition. Prentice Hall.
Statistics II — Course Syllabus
Bachelor’s Degree in Management · Academic Year 2025/2026
ISCAL
Lisbon Accounting and Business School
Polytechnic University of Lisbon
Polytechnic University of Lisbon
Course Information
| Course Unit | Statistics II |
| Area | Data Science and Statistics |
| Course Director | Sofia Delgado António |
| Instructor | Paulo Fagandini |
| pfagandini@iscal.ipl.pt | |
| Lectures | Tuesdays, 11:00 – 14:00 |
| Year / Semester | 2nd Year / 4th Semester |
| Weekly Contact Hours | 3 Hours |
| ECTS | 4 |
General Objective
The objective of this course unit is to present several statistical techniques of great practical use in management. Within the context of random phenomena, students will identify and apply probabilistic models and use the notions of statistical inference to make decisions under uncertainty.
Competencies
Students are expected to acquire and reinforce fundamental concepts of Probability and Statistics. They should become proficient in the main techniques of statistical inference, supported by probability theory, with the primary goal of applying appropriate statistical methods and models to obtain conclusions that support decision-making in business contexts.
Learning Outcomes
Upon completion of this course, students should be able to:
- Infer characteristics of a population from a sample, applying point and interval estimation techniques;
- Understand the general procedures for applying parametric hypothesis tests;
- Understand the specification and underlying assumptions of the linear regression model for cross-sectional data;
- Develop competencies for the joint application of various statistical techniques, using basic software that implements the studied procedures, in order to obtain results that support decision-making under uncertainty.
Syllabus
1. Sampling Distributions
1.1. Central Limit Theorem and applications: Normal approximation to the Binomial and to the Poisson distribution.
1.2. Concepts of random sample and statistic.
1.3. Basic results on the sample mean and sample variance.
1.4. Sampling distributions of the mean in Normal and non-Normal populations. (Includes the t-Student distribution, in the context of this topic.)
1.5. Sampling distributions of the variance in Normal populations. (Includes the Chi-Square distribution, in the context of this topic.)
1.6. Sampling distribution of the proportion from a Bernoulli population.
2. Parameter Estimation
2.1. Point Estimation
2.1.1. Introduction. Basic notions of estimation: point and interval estimation. The concepts of estimator and estimate.
2.1.2. Point estimators. Properties of Estimators.
2.2. Interval Estimation
2.2.1. Basic notions.
2.2.2. Confidence intervals for Normal populations: population mean, population variance, difference between two population means.
2.2.3. Confidence intervals for non-Normal single-parameter populations (large samples).
3. Parametric Hypothesis Testing
3.1. Basic concepts: statistical test, null and alternative hypothesis, test statistic, significance level and critical region. Type I and Type II errors.
3.2. The concept of p-value.
3.3. Tests involving parameters of Normal populations: tests for means and variances.
3.4. Tests for the difference between means of two Normal populations.
3.5. Tests under asymptotic normality conditions (large samples).
4. The Linear Regression Model
4.1. Introduction: Theoretical Linear Regression Model, linear relationships.
4.2. Classical Linear Regression Model for Cross-Sectional Data.
4.3. OLS Estimation Method. Coefficient estimates and their interpretation.
4.4. Properties of the OLS estimators of regression coefficients.
4.5. Goodness of fit: Coefficient of determination and correlation coefficient.
4.6. Statistical Inference: Hypothesis Tests and Confidence Intervals (one parameter).
4.7. Validation of the Classical Linear Regression Model Assumptions (Brief Overview).
Assessment
Assessment may take place under a continuous assessment regime or by final exam.
Continuous Assessment
| Assessment Element | Weight | Duration | Syllabus Content | Indicative Date |
|---|---|---|---|---|
| Written Test 1 | 45% | 1h 20m | Topics 1 + 2.1 | Week of 23–27 March |
| Written Test 2 | 55% | 1h 20m | Topics 2.2 + 3 + 4 | Week of 18–23 May |
- Continuous assessment is based on two (2) written tests, held in person.
- For approval under this regime, students must obtain a minimum grade of 7 (seven) points in each assessment element. Attendance at all assessment moments is compulsory.
- The final grade is the weighted average of the two tests:
\[\text{Final Grade (CA)} = 0.45\,(\text{Test 1}) + 0.55\,(\text{Test 2})\]
- Students under continuous assessment may be subject to an oral examination whenever the instructor deems it necessary to validate the assigned grade.
- No additional minimum attendance requirements are defined beyond mandatory presence at assessment moments.
Final Exam Regime
Students who prefer the final exam regime may sit a comprehensive exam worth 100% of the final grade, covering all course content.
Bibliography
Additional References (Portuguese)
Custódio, S.G.; Ferreira, T.; Morgado, A.J. & Delgado, S. (2023) — Análise de Regressão Linear. Exercícios de Aplicação Geral e Económica. Sílabas&Desafios.
Ferreira, T. & Custódio, S.G. (2023) — Modelos Probabilísticos. Síntese Teórica e Exercícios Resolvidos. Edições Sílabo.
Morgado, A.J.; Custódio, S.G. & Ferreira, T. (2023) — Análise de Regressão Linear. Uma abordagem modelar introdutória. Sílabas&Desafios.
Murteira, B.; Silva Ribeiro, C.; Andrade e Silva, J. & Pimenta, C. (2010) — Introdução à Estatística. Escolar Editora, McGraw-Hill.
Paulino C. & Branco J. (2012) — Exercícios de Probabilidade e Estatística. Escolar Editora.
Pedrosa A.C. & Gama S.M.A. (2004) — Introdução Computacional à Probabilidade e Estatística. Porto Editora.
Pestana, D. D. & Velosa, S. F. (2006) — Introdução à Probabilidade e à Estatística. Vol. I. 2ª edição. Fundação Calouste Gulbenkian.
Pimenta, F., Andrade e Silva, J.; Silva Ribeiro, C. & Murteira, B. (2015) — Introdução à Estatística — 3ª Edição. Escolar Editora.
Robalo A. (2018) — Estatística. Exercícios. Vol. II. 6ª ed. Edições Sílabo.
Wooldridge, J. M. (2009) — Introductory Econometrics. A Modern Approach. 4th Ed. Thomson South-Western.