Knowledge and understanding: Know a basic grounding in the theory and concepts of statistical reasoning, both descriptive and inferential. Know techniques for exploratory data analysis. Understand how to form appropriate scientific questions. Know the basics of probability theory and random variables to help in understanding the techniques of statistical inference. Know the fundamentals of statistical inference. Know the descriptive and inferential aspects of simple linear regression models. Applying Knowledge and understanding: Apply techniques for exploratory data analysis which consists in organizing, displaying and summarizing data. Apply the basics of probability theory and random variables. Apply the fundamentals of statistical inference including the primary tools of estimation, confidence interval construction and hypothesis testing. Apply the descriptive and inferential tools of simple linear regression models.

Mathematics course is introductory to Statistics course (in case of non-compliance Statistics examination will be annulled).

Course Content Summary The course is structured into three parts: Exploratory data analysis Data organization and investigation through frequency distributions, graphical displays, and measures of location, spread and shape. The study of the relationship existing between two variables using two-way frequency tables, scatterplots, and measures of dependence. Regression line: introduction to (simple) linear regression models. Elements of probability Events, axioms of probability, the addition and multiplication rules and associated theorems. Discrete and continuous variables. The main discrete and continuous probability models. Random variables and independence. Transformations and sum of random variables. Elements of statistical inference Introduction to inferential statistics. Sampling distributions. Point and interval estimation and parametric hypothesis testing, mainly focussing on inferences involving the population mean, the population variance and the proportion of successes. Test of independence in two-way tables. Statistical inference applied to the simple linear regression model.

- Cicchitelli G., D'Urso P., Minozzo M., Statistics: Principles and methods con MyLab (2021), Pearson - Agresti A., Franklin C. A., Klingerberg B., Statistics: the art and science of learning from data, Global Edition 5th Edition (2021), Pearson - Newbold P., Carlson W.L., Thorne B., Statistics for Business and Economics, 9th Edition (2019) Pearson/Prentice Hall, Boston

Syllabus Exploratory data analysis Introduction: statistics; scientific method, science, activity; from the world of information to knowledge; descriptive statistics and inferential statistics. Data collection: variables, units and population; census and sample surveys; categorical and numerical variables. Displaying univariate distributions: frequency tables; graphical displays (pie chart, bar graph, histogram, quantile plot, .). Summarizing univariate distributions: measures of location (measures of central tendency, quantiles), spread (range, interquartile range, standard deviation) and shape (symmetry, kurtosis); boxplots. Analyzing the relationship between two variables: two-way contingency tables (joint, conditional, and marginal frequencies), and measures of association (X2, contingency index; relative risk and odds ratio); grouped data and mean difference across groups; scatterplot, covariance and linear correlation, regression line (computation, interpretation, properties, and prediction). Elements of probability Probability: Events. Probability (notes on different definitions), axioms, the multiplication and addition rules. Conditional probability, independent events. The total probability theorem, Bayes theorem. Probability distributions: Univariate discrete and continuous random variables. Density and distribution functions. Joint, marginal and conditional probability distributions. Expected values and variance. Probability models for discrete and continuous variables: Binomial, Poisson, Geometric, Uniform (discrete and continuous), Exponential, Normal (use of tables). Further elements of probability: Introduction to transformations of random variables. Additivity of random variables and linear combinations of random variables. The Law of Large Numbers and the Central Limit Theorem. Elements of statistical inference Introduction to statistical inference: Probabilistic sampling in statistical inference. Simple random sampling. Sample statistics. Sampling distribution of mean and variance of samples from normal populations. Sampling distribution of mean for large samples. Sampling distribution of a proportion. Chi-squared, Student-t and Snedecor-F probability models. Point estimation: Mean squared error. Properties of an estimator (unbiasedness, consistency, efficiency). Interval estimation: Interpretation and construction of confidence intervals. Confidence intervals for the mean of a normal population with known or unknown variance. Confidence interval for a proportion. Confidence intervals for large samples. Hypothesis testing: Null and alternative hypotheses. Type I and type II errors. Levels of significance. Observed significance probability (p-value). Hypothesis tests on the mean, variance and proportion from one population. Hypothesis tests to compare the means, variances and proportions from two populations. Chi-squared goodness of fit test, Chi-squared test of independence. Estimation and hypothesis testing in simple linear regression.

Lectures (60 hours) are alternated with practical sessions (20 hours). The course will make use of teaching tools available on the moodle2, MS/Teams and wooclap platforms, as well as, software as Excel and R.

For attending students, handouts and practical sessions will be made available on Moodle page of the course. Note that Moodle material is to be considered as a guide to the study that must be completed by means of books' chapters (and exercises therein). Those students not attending the classes must necessarily prepare more thoroughly through the textbooks or other statistics texts (topics of this course are basic and covered by any standard statistics book).

The exam consists in a written test. Test text is divided into two parts: a first part consisting of a series of simple questions, theoretical and applied (of immediate calculation), to test the student has sufficiently covered and understood the various topics of the course (they are of T/F, open and multiple choice questions); a second part consisting of two/three exercises of statistical analysis with multiple questions to test the student ability of using appropriate principles and techniques to solve simple statistical problems (examples will be given during the course in form of homework and practical session exercises; textbook exercises are necessary to complete the preparation as well). The first part of the test will be evaluated with a maximum of 21/30 points, while the second part allows to reach grades up to 30/30.

This course covers some topics related to one or more objectives of the 2030 Agenda for the Sustainable Development of United Nations.