# 84555 - STATISTICS

## Conoscenze e abilità da conseguire

Objectives: The course aims at providing students with the main concepts of Statistical Theory and tools of data analysis. These include - exploratory techniques for describing and summarizing data by graphical devices and summary measures, in both univariate and bivariate problems. - inferential methods of point and interval estimation and hypothesis testing in the context of random sampling from Gaussian and Binomial populations. To be able to understand the probabilistic aspects involved in Statistical Inference, students will also acquire knowledge of basic results of Probability Theory. In addition, during lab sessions students will be introduced to the use of the statistical software R for the application of several of the methods covered in the conventional lectures.

## Contenuti

The course program is organized in three parts as described below.

1. Exploratory data analyis
Graphical tools for data analysis and presentation. Frequency tables. Frequency distributions. Summary measures of position and dispersion. Two-way contingency tables. Joint, marginal and conditional distributions. Independence. Association. Linear dependence and correlation.

2. Probability Theory
Approaches to Probability Theory. Axiomatic approach to probability. Sets and Events. Conditional probability. Independent events. Total probability theorem. Random variables. Mean, quantiles and variance. Discrete and Continuous Uniform distribution. Binomial distribuiton. Gaussian distribution. Independent variables. Sums of random variables. Central limit theorem and related results. Chi-squared and t distributions.

3. Inferential Statistics
Random sampling. Parametric statistical inference. Sampling distributions. Point estimation. Bias and mean squared error. Consistency. Confidence intervals for the mean of a Gaussian population. Approximate confidence interval for a probability. Confidence interval for the difference between the means of two Gaussian populations. Hypothesis testing on the mean of a Gaussian population. The p-value. Approximate test on a probability. Test on the difference between the means of two Gaussian populations.

Note: A good knowledge of the contents of the Calculus and Linear Algebra course (or an equivalent 12 cfu Mathematics course) is essential to follow the lectures.

## Testi/Bibliografia

• Anderson, D.R., Sweeney, D.J., Williams, T.A., Freeman, J., Shoesmith, E. (2017), Statistics for Business and Economics, Cengage Learning EMEA, Andover, UK. 4th Edition.

• Lecture notes for Module 1 are  available on Piazza at the site https://piazza.com/unibo.it/fall2019/84555/, while for Module 2 they can be found on IOL

## Modalità di verifica dell'apprendimento

Prerequisites

Passing the Calculus and Linear Algebra exam (or an equivalent 12 cfu Mathematics exam) is a prerequisite for taking the Statistics exam.

Format

Written examination. The full exam will comprise exercises and theoretical questions on all the topics covered in class. Examples of past exam papers will be made available at the beginning of the course.

Students taking the first mid-term exam can sit the second mid-term exam only if they obtained a sufficient mark. The second-midterm can be taken only once either right at the end of the course or on the following call. If the student fails the second midterm, he/she will have to resit the full exam and will lose the grade obtained in the first mid-term. For students taking both midterms, the final mark is the average of the grades obtained in the two midterms.

In some cases, after the full or second midterm exam, the lecturer may require an oral exam as a further tool of assessment of the student's preparation.

Students can reject the grade obtained at the exam once. To this end, he/she must email a request to the instructor within the date set for registration. The instructor will confirm reception of the request.

Rejection is intended with respect to the whole exam. If the grade is rejected, the student must retake the full exam. The only grade that can be rejected without any communication from the student is the first midterm one: in this case the student can either take the second midterm or sit the full exam (thus losing the grade obtained in the first midterm).

## Strumenti a supporto della didattica

Teaching material (lecture notes, exercises, past exam papers, etc) and further information about the course will be made available at the beginning of the course.

Some numerical examples will be carried out using the statistical software R which can be freely downloaded from the web page http://www.r-project.org/

## Orario di ricevimento

Consulta il sito web di Paola Bortot

Consulta il sito web di Emanuel Guariglia