# Statistics I

**Business Administration (pós-laboral)**, Publication in the Diário da República - RCC 01/04/2011 [DR.7678/2011 26.05.2011]

4 ECTS; 1º Ano, 2º Semestre, 45,0 TP

**Lecturer**

**Prerequisites**

Not applicable.

**Objectives**

The students should gain a critical mindset and have a good degree of autonomy in data analysis and decision-making. Particular emphasis is placed on the analysis of economic data.

**Program**

1. DESCRIPTIVE STATISTICS

1.1. Importance and goals of Statistics. Data analysis method steps.

1.2. Characterization data.

1.3. Frequency distributions.

1.4. Measures of descriptive statistics

1.4.1. Measures of location: central tendency (mean, median and mode) and measures of position (quartiles, deciles and percentiles). Identification and classification of outliers. Box-plot.

1.4.2. Measures of dispersion.

1.4.3. Measures of skewness.

1.4.4. Measures of kurtosis.

2. PROBABILITY THEORY

2.1. Some notes on combinatorial analysis.

2.2. Definitions.

2.2.1. Random Experiments.

2.2.2. Probability space.

2.2.3. Events.

2.3. Properties of set theoretic operations.

2.4. Definition and properties of probability.

2.4.1. Classical definition of probability.

2.4.2. Relative frequency definition of probability.

2.4.3. Axioms of probability.

2.5. Conditional probability.

2.6. Independence events.

2.7. The law of total probability and the Bayes? Theorem.

3. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS

3.1 Random variables.

3.1.1. Discrete random variables. Probability mass function and cumulative distribution function. Expected value, variance and some their properties. Mode and quartiles.

3.1.2. Continuous random variables. Probability density function and cumulative distribution function. Expected value, variance and some their properties. Mode and quartiles.

3.2. Some discrete probability distributions.

3.2.1. Binomial distribution.

3.2.2. Poisson?s distribution.

3.2.3. Poisson approximation to the Binomial distribution.

3.2.4. Other discrete probability distributions: geometric and hypergeometric.

3.3. Some continuous probability distributions

3.3.1. Normal distribution. Definition, properties, using the standardized Normal distribution N(0,1) table.

3.3.2. Central limit theorem. Normal approximation to the Binomial and Poisson?s distributions.

3.3.3. Other continuous probability distributions: Chi-square, Student?s t and Snedcor?s F distributions.

4. ESTIMATION

4.1. Basic concepts of estimation. Estimator and estimation.

4.2. Point estimation.

4.3. Interval estimation for the mean, proportion, variance and difference between means and variance.

5. HYPOTHESIS TESTING

5.1. Introduction to hypothesis tests. Null and alternative hypotheses, one-tailed and two-tailed hypothesis tests, types of errors, significance and power of hypothesis tests.

5.2. p-value method.

5.3 Hypothesis tests for various parameters.

**Evaluation Methodology**

Final written test. A minimum mark of 10 out of 20 exempts students from examination.

**Bibliography**

- Sarsfiels Cabral, J. e Guimarães, R. (2005). *Estatística*. Lisboa: McGraw Hill

- Murteira, B. (2003). *Introdução à Estatística*. Lisboa: McGraw Hill

**Method of interaction**

Theoretical-practical classes where beyond the theoretical exposition of the syllabus, practical applications of the topics presented are developed.

**Software used in class**

Not applicable.