# Statistics

**Year**

1

**Academic year**

2015-2016

**Code**

01000079

**Subject Area**

Mathematics

**Language of Instruction**

Portuguese

**Mode of Delivery**

Face-to-face

**Duration**

SEMESTRIAL

**ECTS Credits**

6.0

**Type**

Compulsory

**Level**

1st Cycle Studies

## Recommended Prerequisites

Mathematical Analysis I.

## Teaching Methods

The teaching is provided in theoretical and practical sessions. The theoretical sessions are expository and include the presentation of examples that motivate and enable to understand the notions exposed. In order to apply the acquired knowledge, exercises are systematically proposed in the practical sessions and students must participate in solving them.

Small projects involving fieldwork, development of simple statistical models and computational means may be suggested to develop critical skills and interpretation of results.

Weekly, tutorial time is offered to help students to overcome their learning difficulties.

## Learning Outcomes

The goal is to introduce basic knowledge to prepare the student to model the behavior of random phenomena in the context of engineering or science. It contributes to prepare students to describe, analyze and interpret real situations using non-deterministic mathematical models. The correct use of statistical methods in specific cases, and the strict interpretation of results, requires a theoretical base, for which this course contributes

It intends to prepare students for applying statistical methods and concepts to real situations involving the estimation of parameters of a model, testing its fitness and getting explanation to interpret, predict and decide on the phenomena under study.

This unit develops the following instrumental skills: analysis and synthesis, problem solving and decisionmaking capacity. On a personal level: development of critical thinking, work in interdisciplinary teams, autonomous learning, adaptability to new situations and application of theoretical knowledge

## Work Placement(s)

No## Syllabus

Probability

Random experience, the space of outcomes, events. Kolmogorov’ definition of probability and its consequences. Conditional probability. Independence of events.

Random Variables and Distributions

Discrete and continuous real random variables. Simple and centered moments. Order parameters. Principal discrete and continuous probabilistic models. Central limit theorem and applications.

Parametric Estimation

Introduction to inferential statistics. Review of descriptive statistics. Point estimation: estimators, properties of the empirical mean and variance, point estimation methods. Interval estimation: confidence intervals, the method of the pivotal variable, applications.

Hypothesis Tests

Introduction to the theory of hypothesis testing. Parametric tests. Applications. Chi-square test of adjustment.

Simple Linear Regression Model

Construction and validation of the model. Confidence intervals and tests for the parameters of the model. Forecasting.

## Head Lecturer(s)

Cristina Maria Tavares Martins

## Assessment Methods

Assessment

*There are 2 types of grading: during the semester or by final examination. Grading during the semester may involve problem solving or the development of a project (weighting from 0 to 40%), taking tests (with 0-30% total weight) or midterm exams (with 50-100% weight). Grading by final examination includes taking a written exam (weighting 50 to 100%).: 100.0%*

## Bibliography

• Gonçalves, E., E. Nogueira, A.C. Rosa (2011) - *Noções de Probabilidades e Estatística*, 183 p. Departamento de Matemática, FCTUC.

• Murteira, B., C. S. Ribeiro, J. A. Silva, C. Pimenta (2010) - *Introdução à Estatística*, 3ª ed., Escolar Editora, Lisboa.

• Andrews, L.C., R.L. Phillips (2003) – *Mathematical Techniques for engineers and scientists*, Spie Press, Washington.

• Devore, J.L. (2011) -** Probability and statistics for engineering and the sciences**, 8ª ed., Brooks/Cole.

• Guimarães, R., Sarsfield Cabral, J. (2007) - *Estatística*, 2ª ed., McGraw-Hill, Lisboa.

• Maroco, J. (2007) - *Estatística com utilização do SPSS*, 3ª ed., Edições Sílabo.

• Montgomery, D.C., G.C. Runger (2007) - *Applied Statistics and Probability for Engineers*, 4ª ed., 2007, Wiley.

• Moore, D., McCabe, G. (2011) - *Introduction to the practice of statistics*, 7ª ed., Freeman, New York.