BASIC STATISTICS AND PROBABILITY
6 ECTS credits (4 Boston U. credits)
Good background in High School Algebra
Attendance is compulsory. All exams are required. Make up exams will be given only under very special circumstances.
Prof. Patricio Cifuentes
Department: Matemáticas
Building/office: Ciencias / Módulo 17, room 404
Email: patricio.cifuentes@uam.es
Web page: http://www.uam.es/patricio.cifuentes
Office hours: M Th W Th 15:30-16:30
Ms. Elena Sofía Nieto
Department: Matemáticas
Building/office: Ciencias / Módulo 17, room 613
Email: elenas.nieto@uam.es
The main aim of this course is to introduce the student to the basic statistical concepts that will permit a first approach to the descriptive and the inferential statistical tools, giving enough background to interpret the basic Statistics results found in scientific papers. The course is completed with a short introduction to the elementary concepts in Probability, essential to give a scientific foundation to Mathematical Statistics. These general objectives may be summarized in the following four points:
Introduction to the basic Statistical tools to analyze data proceeding from a variety of sources.
Introduction to the basics of Probability.
Ability to read and understand statistical texts from several scientific areas.
Use of basic computing statistical tools.
DESCRIPTIVE STATISTICS: Graphical and numerical representation of quantitative data. Paired data: correlation coefficient.
PROBABILITY MODELS AND SAMPLING: Discrete random variables. Bernoulli trials. Binomial distribution. Continuous random variables. Uniform distribution. Normal distribution. Sampling. Estimators. Distributions related to the normal distribution: Chi square, Student's t, F.
POINT ESTIMATION: The concept of a point estimator. Properties. Criteria to determine good point estimators.
CONFIDENCE INTERVALS: Constructing confidence intervals. Confidence intervals for proportions. Confidence intervals for means in normal populations. Paired data. Approximate intervals from large samples. Minimum sample size.
HYPOTHESIS TESTING: Setting of the problem. Null and alternative hypothesis. Type I and Type errors. Significance level and rejection set. Tests for ratios. Tests for mean in normal populations. Paired data. Relationship between confidence intervals and hypothesis testing. What is the p-value? Non-parametric tests: goodness of fit.
Textbook
Other texts
The course will meet 4 hours per week. The material of the course will be covered during two of these four hours. The other two hours will be dedicated to discussing and solving exercises, using specialized computer software, and doing exams and quizes. You will need to bring to class a calculator.
A list of homework exercises is given below. It is important to work out these exercises. They cover the essential parts of the course. You will be asked to turn in only some of the exercises. Homework can be worked out in groups but should be turned in individually.
This subject web page, where all the information on this page is mantained, is
http://www.uam.es/patricio.cifuentes/BS&P/index.html
The course material will be kept and updated at
https://moodle.uam.es/
where only registered students will bew able to access.
Students are supposed to dedicate 6 hours per week to personal study and work.
During the semester, two quizzes and a midterm will be given. The final grade will be determined as follows: the final exam will count 40%, the midterm will count 30%, each quiz will count 15%.
Week 1: Sep 10th. Intro; overview; Statistics, what is it? Types of data.
Week 2: Sep 17th. Data description, summaries. Diagrams, plots, numbers
Week 3: Sep 24th. Quiz 1. Intro to Probability, elementary problems.
Week 4: Oct 1st. A more formal approach to probability.
Week 5: Oct 8st. Random variables. Discrete random variables.
Week 6: Oct 15th. Bernoulli trials, binomial distribution.
Week 7: Oct 22th. [ Organic Chemistry Lab ]
Week 8: Oct 29th. Review session. Midterm.
Week 9: Nov 5th. Continuous random variables. Uniform and normal distributions.
Week 10: Nov 12th. Sampling and the Central Limit Theorem.
Week 11: Nov 19th. Point and interval estimation. Means and Proportions.
Week 12: Nov 26th. Quiz 2. Hypothesis testing.
Week 13: Dec 3rd. Hypothesis testing for the mean, known variance.
Week 14: Dec 10th. Hypothesis testing for mean and variance.
Week 15: Dec 17th. Two-sample inferences, equal variances. Final exam.