00914 - Statistics

Learning outcomes

The aim of the course is to provide basic tools for analyzing and describing a set of data through numerical indexes and graphical representations for both univariate and bivariate data. The student will be able to deal with basic tools of probability theory and its applications. The student 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

First Part -  Descriptive statistic

Some definitions: statistical survey, data set, population, sample, variables, parameter, statistic. Classification of variables. Graphical representations. Individual and frequency distributions. Histogram and empirical distribution function. Measures of location, dispersion and shape. Means, median, standard deviation, variance. Covariance and correlation coefficient. Linear dependence and independence. Linear regression model.numbers.

Second Part -  Probability

Events. Probability. Axioms of probability. Conditional probability and stochastic independence.  Bayes theorem. Random variables. Probability distribution. Probability and density functions: uniform, Bernoulli, binomial, Poisson, Gaussian, t-Student, chi-square, Fisher. Expected value and variance. Linear combination of random variables. Independent random variables. Central Limit Theorem.

Third Part -   Statistical inference

Random sampling. Statistics and sampling distributions. Point estimation, confidence intervals and hypothesis testing. Unbiased and efficient estimator. Mean square error. Consistency. Sample mean. Sample variance. Estimator for a proportion. Confidence interval and hypothesis testing for the mean of normal and non-normal population in case of both known and unknown variance. Confidence interval and hypothesis testing for the proportion. Confidence interval and hypothesis testing for difference of means of two independent populations in case of known and unknown variances. Confidence interval and hypothesis testing for difference of proportions of two independent populations

Readings/Bibliography

P. Newbold, W.L. Carlson e B. Thorne (2007) Statistica, Pearson-Prentice Hall (versione italiana).

Further suggested books:

S. Borra e A. Di Ciaccio (2008) Statistica. Metodologie per le Scienze Economiche e Sociali (II ed.), McGraw-Hill.

G. Cicchitelli (2008) Statistica - Principi e Metodi, Pearson Education

Teaching methods

Full frontal class.

Assessment methods

Written exam and oral exam (optional).

Teaching tools

Course notes downloadable from the lecturer's web page.

Links to further information

http://www2.stat.unibo.it/lupparelli/

Office hours

See the website of Monia Lupparelli