# Statistics II

## Objectives

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 the 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 procedure.

## General characterization

##### Code

100055

##### 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

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

### Bibliography

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

Carvalho, A. (2015). *Exercícios de Excel para Estatística*. FCA - Editora de Informática.

Hogg, R. V., Tanis, E. A. (2010). *Probability and Statistical Inference*. 8th Edition, New Jersey: Pearson/Prentice-Hall.

Newbold, P., Carlson, W. L., Thorne, B. (2012). *Statistics for Business and Economics*. 8th Edition, Boston: Pearson.

Murteira, B., Ribeiro, C.S., Silva, J.A. e Pimenta, C. (2002). *Introdução à Estatística*. McGraw Hill.

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

### Teaching method

The curricular unit is based on theoretical-practical classes and practical classes. The practical part of the course is aimed at solving problems and completing exercises. It is also proposed an exercise book that should be solved with individual work in the tutorial sessions of some practical classes and out of classes.

### Evaluation method

1st call: three in-class tests (1/3 weight each), and it is required a minimum score of 9 points in two of the tests (0-20 scale).

2nd call: final exam (100%).

## Subject matter

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

LU1: Sampling distributions: concepts; Central Limit Theorem; distribution of the sampling mean, difference between means, variance, ration 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: