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

This course provides a comprehensive introduction to data analysis and statistical inference, equipping students with the fundamental tools to describe, interpret, and model both univariate and bivariate data using numerical indexes, graphical techniques, and dependence models. The first part of the course focuses on exploratory data analysis and probability theory, including distributions, expected values, and key theorems. The second part covers statistical inference, guiding students through estimation techniques, confidence intervals, and hypothesis testing. The final part introduces linear regression and correlation analysis, preparing students to apply statistical reasoning to real-world problems in economics and business.

Structure of the course:

1 Fundamental concepts: populations and parameters, samples and statistics, quantitative and qualitative data.

2 Graphical presentations of different types of data: pie charts and bar charts; frequency diagrams, stem-and-leaf plots, histograms.

3 Measures of position: arithmetic mean, median, mode, quantiles. Measures of dispersion: variance and standard deviation, range, interquartile range.

4 Coefficient of variation. Box-and-whisker plot. Skewness and kurtosis coefficients. Use of R.

5 Random experiment, sample space, and random events. Definitions of probability. Properties of probability: addition and multiplication.

6 Conditional probability and independence. Bayes' theorem. Joint probability.

7 Unidimensional discrete and continuous random variables. Probability, distribution, and density functions. Expectation and variance.

8 Joint and marginal probability distributions. Independence. Covariance and correlation of random variables.

9 Discrete probability distributions: Poisson and Bernoulli.

10 Continuous probability distributions: uniform and normal.

11 Random sample. Parameter and estimator. Sampling distribution of the mean for samples from a normal population with known and unknown variance.

12 Central Limit Theorem. Distribution of the variance for samples from a normal population. Interval estimation.

13 Confidence interval for the mean of a normal random variable with known/unknown variance.

14 Confidence interval for the variance of a normally distributed random variable. Concept of parametric hypothesis testing.

15 Hypothesis test for the mean of a normal population with known variance. Hypothesis test for the mean of a normal population with unknown variance. p-value. Types of error.

16 Teorema de Tchebychev. Relación entre test de hipótesis bilateral e intervalo de confianza.

17 Hypothesis test for the variance of a normal population. Sample size.

18 Simple linear regression model. Least squares method for estimating regression line parameters. Gauss-Markov assumptions.

19 Analysis of model residuals. Goodness of fit. Use of R.

20 Confidence intervals and hypothesis tests. Correlation analysis. Use of R.

Readings/Bibliography

Required Readings:

- Anderson, D.; Sweeney, D.; Williams, T., Estadística para Administración y Economía, 2008, CENGAGE Learning

Supplementary Readings (Optional):

• Bacchini, D. et al. Introducción al Probabilidad, 2018. Universidad de Buenos Aires, Facultad de Ciencias Económicas.
• Newbold, P.; Carlson, W.; Thorne, B., Statistics for Business and Economics. 2013. Pearson, USA

Teaching methods

- Lectures

- Problem-based learning

Assessment methods

The course will be assessed through two written exams.

Component Weight (%)

Midterm Exam 50

Final Exam 50

- Midterm/final structure:

Examinations are written assessments in which students are expected to solve a series of exercises related to the course content. Each exercise carries a predetermined maximum point value, which is awarded upon correct completion and thorough justification of all steps involved.

The evaluation of the exam answers depends on the correctness, completeness, and rigor of the responses provided.

- Exam policy:

Students who maintain regular status will be automatically enrolled in the corresponding exam sessions; no separate registration is required.

Students who achieve a grade of 18 or higher in the first mid-term exam will be exempt from retaking the content assessed in that exam during the first final examination. However, if they do not pass the first final exam, they must take a comprehensive final exam covering all course content in either the second or third final exam sessions.

After each examination, a date will be scheduled for the publication of grades and for a review session. Students may reject the grade obtained, but this option can only be exercised once. In such cases, the original grade will be irrevocably replaced by the grade earned in the next examination call.

Grading scale:

< 18: failed

18-23: sufficient

24-27: good

28-30: very good

30 e lode: outstanding

Students with disability or specific learning disabilities (DSA) are required to make their condition known to find the best possible accommodation to their needs.

Teaching tools

- Learning Platform: Virtuale (virtuale.unibo.it), where slides and assignments are available

- Presentation Software: PowerPoint

- Communication Tools: Email, and the Forum on Virtuale

- Additional Digital Tools/Software: Students will receive guidance on using R to solve statistical problems and interpret results accurately. To encourage active engagement, they are expected to bring their mobile phones to these sessions.

Office hours

See the website of Maria Silvia Moriñigo