Statistics

Code:

EIG0072

Acronym:

EST

Keywords
Classification	Keyword
OFICIAL	Quantitative Methods

Instance: 2020/2021 - 1S

Active?	Yes
Responsible unit:	Department of Industrial Engineering and Management
Course/CS Responsible:	Master in Engineering and Industrial Management

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEGI	89	Syllabus since 2006/2007	2	-	6	56	162

Teaching language

Portuguese

Objectives

This course unit aims to allow students to consolidate knowledge on Descriptive Statistics, Probability Theory and Probability Distributions. To develop new knoeledge on the important field of Statistic Inference, including Random Sampling and Sampling Distributions, Point and Interval Estimation, Hypothesis Testing and Non-Parametric Tests.

Later, on course unit Multivariate Statistics, students will be asked to recall this knowledge in order to learn advanced statistics techniques, which will have an important application in their future career.

Learning outcomes and competences

At the end of the semester, students should be capable of:

• identifying the concepts of this course unit in a structured way;
• using descriptive statistics tools in the analysis of data samples;
• solving common problems, which involve elementary probability theory, random variables, probability distributions, point and interval estimation andstatistical hypothesis testing (parametric and nonparametric);
• using spreadsheets to solve the above mentioned problems.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic spreadsheets skills.

Program

1. INTRODUCTION TO STATISTICS: Data and Observations. Populations and Samples. Statistical Method.


2. DESCRIPTIVE STATISTICS: Types of Data and Measure Scales. Summarizing Categorical, Quantitative and Bivariate Data.


3. SPREADSHEET ENGINEERING AND INFORMATION VISUALIZATION: Spreadsheet Engineering. Information Visualization.


4. PROBABILITIES: Random Experiments. Sampling Spaces and Events. Probability, Conditional Probability and Independence. Total Probability and Bayes Theorems.


5. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: Random Variables. Discrete and Continous Random Variables. Mass, Density and Cumulative Probability Functions. Population Parameters. Joint Probability Distributions. Covariance and Correlation. Transformed Variables.


6. MAIN DISCRETE AND CONTINUOS DISTRIBUTIONS: Binomial, Negative Binomial, Hypergeometric and Poisson Distributions. Uniform, Exponential and Normal Distributions. Chi-square, t and F Distributions.


7. SAMPLING AND SAMPLING DISTRIBUTIONS: Sampling and Random Sampling. Sampling Distributions. Central Limit Theorem. Generation of Random Samples and Sampling Distributions with Spreadsheets. Introduction to Monte Carlo Simulation.


8. ESTIMATION AND CONFIDENCE INTERVALS: Estimators and Estimates. Desirable Properties os Estimators. Estimation Methods. Confidence Interval. Confidence Intervals for Expected Values, Variances and Proportions. Sample Size Determination.


9. STATISTICAL HYPOTHESIS TESTING: Statistical Inference Logic and Scope. Hypothesis Testing Methodology. Significance Level and Statistical Power (Type I and Type II Errors). Relationship between Hypothesis Testing and Confidence Intervals. Hypothesis Testing concerning Expected Values, Variances and Proportions.


10. NON-PARAMETRIC TESTS AND RESAMPLIG STATISTICS: Goodness of Fit Tests. Median Localization Tests. Other Non-Parametric Tests. Bootstrapping Confidence Intervals. Randomization Tests.

Mandatory literature

A. Miguel Gomes, Armando Leitão e José F. Oliveira; Estatística - Apontamentos de Apoio às Aulas, 2019
Guimarães, R. M. C. e J. A. Sarsfield Cabral; Estatística, Verlag Dashöfer Portugal, 2010. ISBN: 978-989-642-108-3

Complementary Bibliography

Nathan Tintle, Beth L. Chance, George W. Cobb, Allan J. Rossman, Soma Roy, Todd Swanson, Jill VanderStoep; Introduction to Statistical Investigations, Wiley, 2015. ISBN: 978-1-119-15430-3
Jay L. Devore, Kenneth N. Berk; Modern mathematical statistics with applications. ISBN: 978-1-4614-0390-6
Thomas Wonnacott, Ronald J. Wonnacott; Introdução à estatística. ISBN: 85-216-0039-9

Teaching methods and learning activities

Methods and techniques are introduced using systematically practical examples. The learning process is complemented with problem solving sessions supported by computer software and two teamwork assignments.

Software

Folhas de Cálculo

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Probability theory

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	65,00
Teste	15,00
Trabalho prático ou de projeto	20,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Elaboração de projeto	50,00
Elaboração de relatório/dissertação/tese	16,00
Estudo autónomo	40,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Admission criteria set according to Article 4 of General Evaluation Rules of FEUP.

Calculation formula of final grade

The final mark (CF) will be obtained by the following formula:
CF = 0.15 FA + 0.20 TG + 0.65 EF

FA - Quizzes:
- 6 quizzes (pratical classes);
- the quizzes mark (FA) is obtained by the average of the best 4 marks achieved by each student.

TG - Teamwork assignments:
- 2 small size teamwork assignments (TG1 and TG2).
- the teamwork assignments mark (TG) is obtained by the following formula: TG = 0.5 TG1 + 0.5 TG2.

EF - Final Exam
- written exam.

To pass this course, apart from a final grade no less than 10, is required a minimum grade of 7 in the final exam.

Special assessment (TE, DA, ...)

Special evaluations will be made by a written exam.

Classification improvement

Students may choose between:

- improving simultaneously components Quizzes (FA) and Final Exam (EF);

- improving only component Final Exam (FE).

Component teamwork assignments (TG) is not possible to improve.