1. Identification and allocation of the Curricular Unit

School

Escola de Ciências Humanas e Sociais

Department

Economia, Sociologia e Gestão

Course code

81

Course denomination

Lic. em Economia

Curricular Unit code

13060

Curricular Unit denomination

Estatística aplicada à economia e gestão

Teacher in charge

Name

Category

Sandra Cristina Pires Dias

Professor Auxiliar

Other teachers from Curricular Unit

Names

Categories

Sandra Cristina Pires Dias

Professor Auxiliar

2. General information

Teaching load / contact hours / ECTS

Autonomous work (hours)

Distribution of contact hours

Total (hours)

ECTS

96.00

OT

TP

6.00

60.00

162

6.00

Schedule of classes

1º semestre:

OT - turma 1
Wednesday at 16h00m with duration of 02h00m
Wednesday at 16h00m with duration of 02h00m
Wednesday at 16h00m with duration of 02h00m

TP - turma 1
Monday at 16h00m with duration of 02h00m
Wednesday at 11h00m with duration of 02h00m

TP - turma 2
Monday at 14h00m with duration of 02h00m
Wednesday at 09h00m with duration of 02h00m

Hours to students attendance

Sandra Cristina Pires Dias - 1º Semester

Begin

Duration

Location

From

To

Segunda, 10h00

02h15

F1.19 (ECT - Polo II)

23/09/2019

18/01/2020

Terça, 14h15

02h15

F1.19 (ECT - Polo II)

23/09/2019

18/01/2020

Quarta, 14h15

01h30

F1.19 (ECT - Polo II)

23/09/2019

18/01/2020

3. Objectives, syllabuses and teaching methods

Curricular Unit objectives and skills to develop (max. 1000 characters)

The aim of this curricular unit is to give students a background in Probability and Statistics. It is intended that students understand the concepts of probability, recognize and use several probabilistic models.
Learning methods of statistical inference and its application to real problems, should allow the students to understand the concept of sampling distribution; obtain confidence intervals and perform hypothesis testing, given its suitability for the problem at hand.

Syllabus (max. 1000 characters)

1. Random variables
Introduction
Discrete random variables: probability function; distribution function; mean, variance and theirs properties; quantiles
Continuous random variables: density function; distribution function; mean, variance and theirs properties; quantiles
Discrete distributions: Binomial, Hypergeometric, Geometric and Poisson
Continuous distributions: Uniform, Exponential, Normal, Chi-square and t of Student
Central limit theorem
2. Parametric estimation
Introduction
Point estimation
Method of moments and maximum likelihood
Confidence intervals
3. Parametric tests
4. Non parametric tests: normality tests, chi-square test for fitting, homogeneity and independence, Wilcoxon test and Mann-Whitney-Wilcoxon test

Planning teaching activity (according to school Schedule) - (optional)

_

Demonstration of the Curricular Unit syllabus coherence with the intended learning outcomes (max. 1000 characters)

The structure of this course is constructed so that students acquire the basic concepts of Probability and Statistics.
The modeling of random phenomena and quantification of the uncertainty associated with them is discussed in the first sections through the study of probability and random variables, with particular emphasis on probabilistic models commonly used.
The statistical inference is the subject of study in the remaining sections. Starting with the introduction of basic concepts, point estimate is approached, as well as the construction and interpretation of confidence intervals, the statistical testing of hypotheses and decision making.

Teaching / learning methodologies used (working methods, Curricular Unit running, resources, etc..) (max. 1000 characters)

Theoretical-practical classes, taught by oral and written means and multimedia projection, in which the concepts and ideas essential to the process of learning the curricular unit are introduced. Whenever possible, illustration examples will be provided to clarify the exposition of theoretical concepts. Also, in these classes students will be asked to solve practical proposed exercises, requesting the support of the teacher whenever needed.
Tutorial classes in which will be discussed some of the problems to solve.

Demonstration of the consistency of teaching methodologies with the objectives of the Curricular Unit (max. 3000 characters)

The course is organized in a typology of theorical-practical classes and tutorial classes. Some classes, of expositive nature, the concepts will be introduced and its usefulness discussed. It is require from students a component of individual study in order to deepen the knowledge presented contents. In the other classes students will be encouraged to participate more actively in the learning process, testing their knowledge by solving appropriated practical exercises. It is expected that the student develops skills of autonomous and group work.

4. Evaluation Methodology

Assessment modes, need to register prior to testing and transition conditions between modes

Concerning the assessment model of the course unit, the students must take into account the following items.

1. Registration in the course unit
The registration on the lectures (T) and theoretical-practical classes (TP) is mandatory and must be done in the SIDE (Information System for Education Support).

2. Registration in assessment tests
To obtain access to any assessment test, the students should make their registration in the SIDE 48 hours before the corresponding test.

3. Assiduity
To have access to any written test, students must attend a minimum of 70% of the planned contact hours of given classes. Exception made for students with special statutes and students that attended such minimum of classes in 2018-2019.

4. Modes of assessment
The students can be assessed in the following ways:
Mode 1: continuous assessment;
Mode 2: continuous assessment followed by complementary assessment;
Mode 3: final assessment (by exam).

5. Transition conditions between modes
All students who attended at least 70% of the contact hours summarized are admitted to Mode 1 of evaluation, except for students with special status or students with a frequency obtained in the 2018-2019 school year.
Are admitted to Mode 2 students not approved in Mode 1 and who have obtained:
- at least 9.5 values in one of the assessment tests, or
- at least 9 values in one of the assessment tests and at least 6 values in the other test.
Students not approved in Mode 1 and 2 who meet the minimum conditions for access to the exam are admitted to Mode 3 of evaluation.

6. Access to 2nd exam epoch
The students not approved in the 1st exam epoch and that meet the minimal conditions to exam access may be evaluated on the 2nd exam epoch.
To have access to this exam, the students need to enroll in the SIDE.

7. Access to special exam epoch (3rd exam)
The students regularly enrolled in the CU and that meet the conditions described in the Pedagogical Regulation have access to the special (3rd) exam.
To have access to the exam, the students need to enroll in the Academic Services, as well as in the SIDE.

8. In either assessment modes, the students that obtained a classification greater or equal to 17 points, and are seeking for a final grade higher than 17, will have to validate the classification with an additional examination rated for 3 points. The final grade is 17 plus the classification of the additional examination.

9. In any written examination,
(a) the students must have an identification document;
(b) is not allowed to consult any notes and/or books;
(c) is allowed to use a calculator;
(d) is not allowed to use pencil and corrector pen in the test sheet;
(e) the students can not leave the room, in any case, during the time of the examination;
(f) a student wishing to give up must declare it, in writing, on the test sheet, and can only leave the examination room after permission of the teacher and not earlier than 30 minutes after its start;
(g) is allowed the examination to students that arrive to the room until 20 minutes after the examination starts. The student who is granted this permission does not have, for that reason, extra time to finish the examination;
(h) is not allowed all the communication between students that, directly or indirectly, allow to obtain or collect information about the content of the exam;
(i) it is not allowed to use mobile phones or other communications and recording equipment;
(j) fraud or plagiarism imply the annulment of the examination and can bring to the student a disciplinary action.

Minimum criteria for admission to examination

To have access to any written test, students must attend a minimum of 70% of the practical contact hours of classes summarized. Exception made for students with special statutes and students that attended such minimum of classes in 2018-19.
The students that have not been approved in this course and have not attended to a minimum of 70% of the planned contact hours will be considered excluded of this UC in the final of the current year.

Description of evaluation methods, respecting the Article 13 of Chapter IV of UTAD's Pedagogical Regulation (including, scheduling and calculation method).

The continuous assessment (Mode 1) consists of a theoretical-practical component, through the completion of two written tests during the classes period in the following dates:
1st test - October 30, 2019
2nd test - January 17, 2020

Each one of the written tests is rated for 20 points and will last 1 hour and 30 minutes, with a grace period of 30 minutes.

All written tests have the same weight in the final grade; the final classification corresponds to the arithmetic mean of the scores obtained on the two tests

(grade of the 1st test + grade of the 2nd test) / 2

A student will be considered approved in this course unit and dispensed from further evaluation if he obtains a final grade greater than or equal to 9.5 points and if has a classification greater than 9 in one test and greater than 6 in the other test.

The Mode 1 evaluation may also result in admission to Mode 2 or Mode 3 evaluations.

The students are admitted to the Mode 2 assessment if they weren't approved in Mode 1 and obtain:
- a classification equal to or greater than 9.5 points in one of the tests, or
- a classification greater than 9 in one test and greater than 6 in the other test.

The complementary assessment (Mode 2) allows the repetition of the test(s) done in Mode 1, at which the student had a score smaller than 9.5 points, on the 1st date of exam (February 6, 2020). Each test will last 1 hour and 30 minutes, with a grace period of 30 minutes.

The final grade will be computed as described in the continuous assessment, where the classification of the complementary test(s) will replace the classification of the corresponding test(s) in the continuous assessment.

If the students intend to perform the complementary assessment, they should make their registration in the appropriate location on the SIDE.

The students that have been admitted to the complementary assessment and did not appeared to the test or, having appeared, have given up or have been not approved, are admitted to exam to be held in the 2nd exam epoch (February 13, 2020).

The final assessment (Mode 3) consists of a theoretical-practical written test, in which all the syllabus contents explored in the classes are object of assessment on the 1st exam epoch (February 6, 2020). The test is rated for 20 points and lasts for 2 hours with a grace period of 30 minutes.

A student will be considered approved in this course unit if he obtains in the exam a final grade greater than or equal to 9.5 points.

The students not approved in the 1st exam epoch and that meet the minimal conditions may repeat their evaluation on the 2nd exam epoch (February 13, 2020). To have access to this exam, the students need to enroll in the SIDE. The evaluation is carried out in the same way as in the 1st exam epoch.

The students regularly enrolled in the curricular unit and that meet the conditions described in the Pedagogical Regulation have access to the special (3rd) exam. To have access to the exam, the students need to enroll in the Academic Services, as well as in the SIDE.

In either assessment modes, the students that obtained a classification greater or equal to 17 points, and are seeking for a final grade higher than 17, will have to validate the classification with an additional examination rated for 3 points. The final grade is 17 plus the classification of the additional examination.

5. Bibliography

Recommended

Title

Author(s)

Estatística - 2ª edição

Guimarães, R. C., Cabral, J.

Introdução à Estatística

Murteira, B. J., Ribeiro, C. S., Andrade e Silva, J., Pimenta, C.

Introdução à Probabilidade e à Estatística

Pestana, D. D. e Velosa, S. F.

Probabilidades e Estatística para Ciências e Tecnologia

Gonçalves, E., Nogueira, E., Rosa, A.C.

Estatística descritiva e probabilidades, exercícios resolvidos e propostos com aplicações em R

Figueiredo, F., Figueiredo, A., Ramos, A., Teles, P.

Estatística. Exercícios.

Robalo, A.

Applied Statistics and Probability for Engineers

Montgomery, D.C., Runger, G.C.

Introduction to Probability and Statistics for Engineers and Scientists

Ross, S.M.

Introduction to the Theory of Statistics

Mood, A. M., Graybill, F. A. e Boes, D. C.

Complementary

Title

Author(s)

Introdução Computacional à Probabilidade e Estatística