75249 - Statistics (B.A.)

Learning outcomes

At the end of the course students have the basic tools for analysing and describing a set of data through numerical indexes, graphical representations and dependence models for both univariate and bivariate data. The students are able to deal with basic tools of probability theory and its applications. The students will be also able to estimate population parameters from sample data by using standard inferential techniques (point estimation, confidence interval and hypothesis testing).

Course contents

1. Exploratory Data Analysis

Decision making in an uncertain environment. Classification of variables: categorical and numerical variables. Graphs to describe categorical variables: tables and charts, cross tables, pie charts. Graphs to describe numerical variables: frequency distributions, histograms, shapes of a distribution, stem-and-leaf displays.

Measures of central tendency and location: mean, media, mode, percentiles and quartiles. Shape of a distribution.

Measures of variability: range and interquartile range. Box-and-whisker plots. Variance and standard deviation. Coefficient of variation.

Measures of grouped data.

2. Probability

Random experiment, outcomes and events. Definitions of probability: classical probability, relative frequency, subjective probability.

Probability rules. Conditional probability. Statistical Independence. Bayes´Theorem.

Bivariate probabilities.

3. Random Variables and Probability Distributions

Definition of unidimensional random variable.

Discrete random variables: probability distributions, properties. Expected value and variance. Mean and variance of linear functions of a random variable. Bernoulli experiments and the binomial distribution. Jointly distributed discrete random variables. Conditional mean and variance. Covariance and correlation.

Continuous random variables: probability distributions, properties. Expectations. The uniform and normal distributions. Normal distribution approximation for binomial distribution.

4. Sampling Distributions. Estimation: Single Population

Sampling from a population. Sampling distributions of sample means. Central Limit Theorem. Sampling distributions of sampling variances.

Properties of point estimators.

Confidence interval estimators for the mean of a normal distribution: population variance known. Intervals based on the normal distribution. Confidence interval estimators for the mean of a normal distribution: population variance unknown. Intervals based on the Student´s t distribution. Confidence interval estimators for the variance of a normal distribution. Sample-size determination.

5. Hypothesis Testing: Single Population

Concepts of hypothesis testing. Tests of the mean of a normal distribution: population variance known. p-Value. Relationship between two- sided alternative hypothesis and confidence intervals. Tests of the mean of a normal distribution: population variance unknown. Assessing the power of a test. Test of the variance of a normal population.

6. Simple Regression

Overview of linear models. Linear regression model. Least squares coefficient estimators. The explanatory power of a linear regression equation. Coefficient of determination. Satistical inference: hypothesis tests and confidence. Prediction. Correlation analysis.

Readings/Bibliography

Anderson,D.; Sweeney,D.; Williams,T. (2008). Estadística para Administración y Economía. . Cengage Learning, México. https:// [https://www.upg.mx/wp-content/uploads/2015/10/LIBRO-13-Estadistica-para-administracion-y-economia.pdf]www.upg.mx/wp-content/uploads/2015/10/LIBRO-13-Estadistica-para-administracion-y-economia.pdf

Bacchini, R.; Vazquez, L. (2007). Estadística. Probabilidad e Inferencia. Omicron Editorial, Argentina.

Newbold, P.; Carlson, W.; Thorne, B. (2013). Statistics for Business and Economics. Pearson, USA.

https://drive.google.com/open?id=1o5h5lIm7C1JTjRY8ih6bkvhOszXZ_LOD

Teaching methods

Class sessions are a blend of lecture, concept questions and group problem solving. In class group work will be done in groups of four of students´ choosing. Some sessions involve longer problems and the use of R for computation, simulation and visualization. Students need to bring their mobile phones during these sessions.

Assessment methods

Two written examinations.

Teaching tools

Practical class work, slides of the course, materials for self-assessment, R compiler.

Office hours

See the website of Maria Silvia Moriñigo