Course code: 176303 |
Subject title: STATISTICS II |
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Credits: 6 |
Type of subject: Mandatory |
Year: 2 |
Period: 1º S |
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Department: Estadística, Informática y Matemáticas |
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Lecturers |
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ABASCAL FERNANDEZ, ELENA (Resp) | PANIELLO ALASTRUEY, IRENE | ||||

SANTAFE RODRIGO, GUZMAN |

Statistical inference as a tool of making decisions in Economy and Business. Basic notions of probability. Basic concepts of probability. Discrete and continuous probability distributions. Introduction to sampling and sampling distributions. Estimate from sample data. Tests of hypotheses for the population parameters. Estimation and contrast for two populations. Analysis of variance. Nonparametric methods. Application to real data of interest in Economy and Business through a computer program.

- BP2: Students know how to apply their knowledge to their work or vocation in a professional manner and possess skills which are usually demonstrated by developing and defending arguments and resolving problems in their area of study.
- BP3: Students are able to compile and interpret relevant information (normally within their area of study) in order to voice opinions which include reflection on relevant themes of a social, scientific or ethical nature.
- BP4: Students are able to transmit information, ideas, problems and solutions to both specialist and non-specialist audiences.
- GP01: A capacity for analysis and synthesis.
- GP02: A capacity for organisation and planning.
- GP03: Oral and written communication in their mother tongue.
- GP05: Computer skills relevant to the field of study.
- GP07: The capacity to solve problems.
- GP14: Critical and self-critical skills.
- GP17: A capacity for self-reliant learning.

- SP03: To discern information and data relevant to their particular enterprise which a non-professional would be unable to recognise.
- SP04: To analyse business management problems, applying professional criteria based on the use of technical instruments.

At the end of the semester students must be able to:

- Know the possibilities Statistics offer to obtain high-quality information and be able to recognize those situations when statistical analyses are possible and necessary. Differentiate between opinions that can be empirically contrasted and those that cannot.
- Understand statistical terminology.
- Know how to set out an economic problem using statistical terminology. Evaluate properly the difficulties to be overcome in each situation, recognize their limitations and resources.
- Apply Inferential Statistics to problems arising from an economic environment.
- Interpret outcomes and provide conclusions drawn from analyses relating them to the environment data come from.
- Interpret and be able to question reports.
- Develop attitudes favouring the understanding of new statistical procedures that can be useful in other subjects or along the professional career.

More precisely:

Learning outcomes | Contents | Formative activities | Evaluation activities |

Understand the most usual random variables and probability distributions, their properties and those assumptions that make possible to approximate them to the Normal distribution. | Chapters 1 and 2 | Lectures and Practice sessions | In-term tests with and without using computer |

Understand the differences between population and sample. Understand the main sampling distributions and their applications. | Chapter 3 | Lectures and Practice sessions | In-term tests |

Understand those notions arising in Inferential Statistics. Determine the needed sample size to reach required error objectives. Obtain and interpret a confidence interval. Apply the appropriate test for a given problem. Evaluate the quality of the survey reports published by the media. Interpret outcomes provided by statistical software. | Chapters 4, 5 and 6 | Lectures and Practice sessions | In-term tests with and without using computer |

Learning Activities:

Lectures A-1

Practice sessions A-2

Individual or teamwork projects or problem solving A-3

Individual or small group tutorials A-4

Individual work A-5

Exam A-6

Self-evaluation A-7

Lectures will be devoted to introduce the subject basic contents that will be illustrated with practical activities to help students to develop individual-study habits. Lectures and practice session will be alternated for all chapters.

Practice sessions will have two different approaches. Either they will consist of in-class problem-solving sessions of some proposed exercises by the professor or the students or they will consist of practice sessions with computers so that students will be required to use some statistical software as a tool to solve problems and practical cases. Lesson notes as well as any other teaching material will be available in MiAulario.

Proficiency | Activities |

BP2 | A-1, A-2, A-3, A-4, A-5, A-6 |

BP3 | A-1, A-2, A-3, A-4, A-5, A-6 |

BP4 | A-1, A-2, A-3, A-4, A-5, A-6 |

GP01 | A-1, A-2, A-3, A-4, A-5, A-6, A-7 |

GP02 | A-1, A-2, A-3, A-4, A-5, A-6 |

GP03 | A-1, A-2, A-3, A-4, A-5, A-6 |

GP05 | A-1, A-2, A-3, A-4, A-5, A-6 |

GP07 | A-1, A-2, A-3, A-4, A-5, A-6, A-7 |

GP14 | A-1, A-2, A-3, A-4, A-5, A-6 |

GP17 | A-1, A-2, A-3, A-4, A-5, A-6, A-7 |

SP03 | A-1, A-2, A-3, A-4, A-5, A-6 |

SP04 | A-1, A-2, A-3, A-4, A-5, A-6 |

Learning outcomes | Evaluation | Weight (%) | Recoverable |

Understand the most usual random variables and probability distributions, their properties and those assumptions that make possible to approximate them to the Normal distribution. Understand the differences between population and sample, the main sampling distributions and their applications and those notions arising in Inferential Statistics. Obtain and interpret a confidence interval. Determine the needed sample size to reach required error objectives. Apply the appropriate test for a given problem. Evaluate the quality of survey reports published by the media. | In-term tests | 30 % | No |

Apply the appropriate test for a given problem. Interpret outcomes provided by statistical software. All the previous. | Final exam | 70% | Yes |

Continuous evaluation amounts up to 30% of the final mark. The continuous evaluation may include activities such as practice sessions, in-terms tests made with or without a computer, problem solving based on computer-obtained outputs and attendance to office hours. Continuous evaluation activities are not recoverable.

The remaining 70% of the final mark corresponds to the final exam. The final exam will be a written exam about the different theoretical and practical contents of the subject. The final exam may include problem solving, theoretical test-type or essay-type questions or designing how to solve an economic problem using statistical tools.

The aim of this subject is that students learn:

- to consider an economic problem in statistical terms,

- to solve manually and by means of the statistical program R-Commander,

- to correctly interpret the results,

- to elaborate study reports.

This course is devoted to study:

- The main distributions of probability

- Statistical inference.

CHAPTER 0. Basic notions of Probability.

CHAPTER 1. Discrete random variables and probability distributions

- Discrete random variables

- Probability distributions for discrete random variables: probability and distributions functions.

- Characteristics of discrete random variable: expectancy and variance

- Binary and Binomial distributions

- Poisson Probability distribution

- Other distributions

CHAPTER 2. Continuous random variables and probability distributions

- Continuous random variables

- Probability distributions for continuous random variables: density and distribution functions.

- Characteristics of continuous random variable: expectancy and variance

- Normal distribution

- Normal distribution approximation for Binomial and Poisson distributions

- Other distributions

CHAPTER 3. Introduction to Statistical inference and Sampling

- Statistical inference as a tool of decision making

- Concepts of sampling

- Sampling with replacement and sampling in finite populations

- Main sampling distributions: sample mean and sample proportion

CHAPTER 4. Estimation

- Point estimation

- Desirable properties of an estimator

- Estimation methods

- Confidence interval estimation: confidence level and error margin

- Confidence interval estimation for single population parameters

- Confidence interval estimation for comparing two populations' parameters

- Sample size determination

- Estimation using a statistical software

CHAPTER 5. Hypothesis testing.

- Concepts of hypothesis testing

- Parametric tests for single population parameters

- Parametric tests for comparing two populations' parameters

- Analysis of variance

- Hypothesis testing using a statistical software

CHAPTER 6. Nonparametric statistics.

- Introduction to nonparametric methods

- Goodness-of-fit tests

- Independence test

- Tests for comparing two populations

- Nonparametric hypothesis testing using a statistical software

**Acceda a la bibliografía que su profesor ha solicitado a la Biblioteca.**

Basic text

Newbold, P, Carlson, W.L. y Thorne, B. (2007). Statistics for Business and Economics. 6th Edition. Editorial Prentice Hall.

Newbold, P, Carlson, W.L. y Thorne, B. (2008). Estadística para Administración y Economía. Editorial Prentice Hall.

Mi Aulario will be the course web page providing also a communication channel between instructor and students. There students will find the necessary material for both theorical and computer lab sessions, together with data files and any other additional material.

Additional bibliography:

Levin, Rubin, Balderas, Del Valle y Gómez (2004) Estadística para la administración y la economía. Editorial Prentice Hall.

Lind D. A., Marchal W. G. y Wathen S. A. (2008) Estadística Aplicada a los negocios y a la Economía. Editorial McGraw " Hill