00914 - Statistics

Learning outcomes

Purpose of the course is to give the fundamental tools for the statistic analysis of economic-business data, with particular reference to the tourist sector, for descriptive and interpretative purposes. The student will learn concepts and fundamental notions of the descriptive Statistic, of the theory of the Probability and of the theory of the statistical Inference. For best learning of subjects,  knowledge of senior high schools Mathematics is essential.

Course contents

PART 1: Descriptive Statistic:
Introduction to the Statistic as general methodology for the acquisition and the study of the collective phenomenons. The main phases of a statistic investigation. Total surveys and random sample.Classification schemes for statistical characters: distributions for single modalities, frequency distribuctions. Tabular and graphics representation for simple statistic distributions. Definition and meaning of statistical mean. Chisini's definition mean and his practical applications. The variability of the collective phenomenons. Absolute indexes of variability: variation intervals and average differences from a mean. The comparison among the variability of two distributions: construction of relative indexes of variability.
Analytical representation of a statistic variable or historical series: determination of the trend through the least squares method. Goodness of fit and index of determination.Tabular representation of the double statistic distributions. Meaning of “distributive independence” and correspondent analysis of the existing relationship among two statistic characters. Measures of connection among two characters, based on the comparison among observed and theoretical frequencies: absolute and relative index of Cramer. Study of the dependence “in average” among a variable statistic and another character of any nature: Pearson's correlationn ratio. Definition, meaning and characteristics of Covariance among two statistical variables. Linear Regression and Correlation among two statistical variables.

PART 2: Elements of Probabilities:
Random experiment, space of the events, axioms and law of the union. Conditioned probability and law of the intersection among two events. Elements of combinatorial analysis in random sampling with and without replace. Definition of discrete random variable (R.V.): probability function, Expected value, Variance and their characteristics. Joint distributions, independence and Covariance among two random variables. Some special discrete random variables connected to the random sampling: R.V. of Bernoulli, Binomial, Ipergeometric and their characteristics. Definition of continuous casual variable: an intuitive introduction to the definition of density probability function. Distribuction function. Some continuous random variable: Normal, standardized Normal, t of Student. Central limit theorem and his applications. Asymptotic distributions of the Binomial random variable.

PART 3: Elements of statistical Inference:
Introduction to general principles of statistical Inference. Point estimation of a unknown parameter. Estimators and their main characteristics: unbiased, efficient and consistent estimator. Point estimation of the aritmetic mean, the variance and a percentage. Confidence intervals for aritmetic mean and for percentage, in the simple random sampling with or without replace. Determination of the sample size in estimation of a mean or a percentage, in correspondence of a fixed maximum sampling error.
Integrative part for students under old regulation:  Measures of concentration; two indexes of Gini.

Readings/Bibliography

Prof. Benzi: Lezioni di Statistica . Edizione Pitagora Editrice. Anno 2005.

Prof. Benzi-Betti: La rappresentazione parametrica delle distribuzioni statistiche . Edizione Pitagora Editrice N° 23.

Prof. Benzi-Betti: La rappresentazione analitica delle distribuzioni statistiche . Edizione Pitagora Editrice N° 26 .

Integrativ didactic material and developed exercises are available on main university portal: http://www.polorimini.unibo.it/Polo+Rimini/default.htm

Then click on "Material didactic", "Faculty Economy-Rimini", "Material didactic" of Cesare Benzi.

Teaching methods

To improve the understanding of the theoretical subjects, the lessons are integrated from numerous examples and practical applications, especially in tourist field.

This didactic material, when not included in the recommended texts, is available on line.

Assessment methods

The examination provides an oral interview preceded by a written admission test. The written test, of the middle duration of 2,5 hours, comprises some simple exercises, on the model of those resolved during the course or included in the book and some theoretical questions.

Written test registration is obligatorily on line.
On the contrary oral test registration can be do in informal way the same day of the test, on a special available list in the classroom.

Teaching tools

Links to further information

http://www.polorimini.unibo.it/Polo+Rimini/default.htm

Office hours

See the website of Cesare Benzi