Statistical Inference

Objectives

This curricular unit aims to extend the knowledge acquired in Statistics and Probability Distributions (CU previously named Statistics I), as well as supplying to the students theoretical and practical knowledge about more advanced methodologies on parametric inference. The contents of the curricular unit include inference tools such as statistics, estimators, sampling distributions, point and interval estimation, and hypothesis testing. Additionally, some issues of asymptotic distributions are addressed. The students will acquire competences related to point estimators and their properties, and will learn how to construct confidence intervals and perform hypothesis testing on population parameters, such as the mean, the variance, the difference between means, the ratio of variances, the proportion, the difference between proportions and the correlation coefficient. Moreover, the analysis of variance is introduced. The students should clearly understand the conditions of applicability of each statistical procedure.

General characterization

Code

100161

Credits

6.0

Responsible teacher

Ana Cristina Marinho da Costa

Hours

Weekly - Available soon

Total - Available soon

Teaching language

Portuguese. If there are Erasmus students, classes will be taught in English

Prerequisites

Teaching language: English.

In order to meet the leaning objectives successfully, students must possess knowledge of Statistics and Probability Distributions, Math I and Math II.

Bibliography

Pedrosa, A. C., Gama, S. M. A. (2004). Introdução Computacional à Probabilidade e Estatística. Porto: Porto Editora.

Murteira, B., Ribeiro, C.S., Silva, J.A., Pimenta, C. (2010). Introdução à Estatística. Lisboa: Escolar Editora.

Extra reading bibliography:

Newbold, P., Carlson, W. L., Thorne, B. (2013). Statistics for Business and Economics. 8th edition, Boston: Pearson, https://ebookcentral.proquest.com/lib/novaims/detail.action?docID=5174169 (full text available after login in NOVA IMS network or through VPN connection).

Mariappan, P. (2019). Statistics for Business. New York: Chapman and Hall/CRC, https://doi.org/10.1201/9780429443244 (full text available after login in NOVA IMS network or through VPN connection).

Wilks, S. (1948). Elementary Statistical Analysis. Princeton, New Jersey: Princeton University Press. https://www.jstor.org/stable/j.ctt183q2d4 (full text available after login in NOVA IMS network or through VPN connection).

Afonso, A., Nunes, C. (2011). Estatística e Probabilidades. Aplicações e Soluções em SPSS, Escolar Editora.

Carvalho, A. (2015). Exercícios de Excel para Estatística. Lisboa: FCA ¿ Editora de Informática.

Hogg, R. V., Tanis, E. A. (2001). Probability and Statistical Inference. 6th edition, New Jersey: Pearson/Prentice-Hall.

Teaching method

The curricular unit is based on theoretical and practical lessons. A variety of instructional strategies will be applied, including lectures, slide show demonstrations, step-by-step applications (with and without software), questions and answers, use of gamification tools. The sessions include presentation of concepts and methodologies, solving examples, discussion and interpretation of results. The practical component is geared towards solving problems and exercises, including discussion and interpretation of results. A set of exercises to be completed independently in extra-classroom context is also proposed.

Evaluation method

REGULAR PERIOD (1^st call): 5 quizzes (5%), 1^st test (25%; about LU1), 2^nd test (25%; about LU2 and LU3), exam (45%; about all topics, but more focused on LU4 and LU5).

RESIT PERIOD (2^nd call): final exam (100%).

SPECIAL PERIOD: final exam (100%).

RULES:

- For approval in the 1^st call, it is necessary to obtain a minimum score of 8 points in the exam.

- To complete the tests/exam, students must provide themselves with the form and statistical tables disclosed in Moodle, and also with a scientific calculating machine. Graphic calculating machines are not allowed.

- Each quiz focuses on a learning unit.

- All quizzes are solved in Moodle.

- The quizzes are solved during classes or outside class hours.

- Students are informed in advance of the time available for the resolution of the quiz(s) outside class hours.

Subject matter

The curricular unit is organized in 5 Learning Units (LU):

LU1: SAMPLING DISTRIBUTIONS: concepts; Central Limit Theorem; distribution of the sample mean, difference between means, variance, ratio between variances, proportion, difference between proportions.

LU2: POINT ESTIMATION: the method of maximum likelihood; properties of the estimators.

LU3: INTERVAL ESTIMATION: confidence intervals for the mean, difference between means, variance, ratio between variances, proportion, difference between proportions.

LU4: HYPOTHESIS TESTING: concepts and methodology; hypothesis testing for the mean, difference between means, variance, ratio between variances, proportion, difference between proportions, correlation coefficient.

LU5: ANALYSIS OF VARIANCE (ANOVA): analysis of variance with one factor and fixed effects; multiple comparison tests.

Programs

Programs where the course is taught: