# Estatística II

## Objectivos

This curricular unit aims to extend the knowledge acquired in 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.

## Caracterização geral

100055

6.0

##### Professor responsável

Ana Cristina Marinho da Costa

##### Horas

Semanais - A disponibilizar brevemente

Totais - A disponibilizar brevemente

##### Idioma de ensino

Português. No caso de existirem alunos de Erasmus, as aulas serão leccionadas em Inglês

### Pré-requisitos

Teaching language: Portuguese.

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

### Bibliografia

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.

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.

### Método de ensino

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.

### Método de avaliação

REGULAR PERIOD (1st call):

• 5 quizzes (5%)
• 1st test (25%; about LU1)
• 2nd test (25%; about LU2 and LU3)
• Exam (45%; about all topics, but more focused on LU4 and LU5).

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

SPECIAL PERIOD: final exam (100%).

RULES:

- For approval in the 1st 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 practical classes or outside class hours.

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

## Conteúdo

UA1: DISTRIBUIÇÕES AMOSTRAIS: conceitos; Teorema do Limite Central; distribuição da média, diferença de médias, variância, quociente de variâncias, proporção, diferença de proporções.

UA2: ESTIMAÇÃO PONTUAL: método de estimação da máxima verosimilhança; propriedades dos estimadores.

UA3: ESTIMAÇÃO POR INTERVALOS: intervalos de confiança para a média, diferença de médias, variância, quociente de variâncias, proporção, diferença de proporções.

UA4: TESTES DE HIPÓTESES: metodologia; testes de hipótese para a média, diferença de médias, variância, quociente de variâncias, proporção, diferença de proporções, coeficiente de correlação.

UA5: ANÁLISE DE VARIÂNCIA (ANOVA): modelo de análise de variância a um fator com efeitos fixos; testes de comparação múltipla.