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Module Title: Statistics Type of Module: x PC (Prescribed Core Module) PS (Prescribed Stream Module) ES (Elective Stream Module) E (Elective Module) Level of Module Undergraduate Year of Study 3rd Semester 6th Number of credits allocated 4.5 Name of lecturer / lecturers : Vasilis Koutras Description: The first part of the course includes a review of basic concepts of probability theory and a short introduction in Descriptive Statistics. The second part, presents the fundamental concepts of statistics used to inference effectively on the characteristics of a population based on samples. A random sample is taken from a population and based on this, estimators for the population’s parameters are computed and their accuracy is examined. Additionally, the procedures used to test hypotheses about a population are presented. To this direction, the course focuses on estimation theory, confidence intervals, hypothesis testing, non-parametric test. Finally, the basic concepts of linear regression are also presented. Prerequisites: None (student must be familiar with topics in Probability Theory) Module Contents (Syllabus): Week 1. Week 2. Week 3. Week 4. Week 5. Week 6. Week 7. Week 8. Week 9. Week 10. Week 11. Week 12. Introduction-Probability Theory, Distributions and moments-Exercises Sample distributions, Student distribution, χ2 distribution, F distribution-Exercises Sampling, Central Limit Theorem-Exercises Descriptive statistics Estimation, Unbiased Estimators (bias, consistency, adequacy, completeness)-Exercises Estimator of minimum variance-Exercises Maximum likelihood estimators-Exercises Confidence intervals-Exercises Hypothesis testing for the mean Exercises in hypothesis testing for the mean Hypothesis testing for binomial p, difference of means, variance-Exercises Goodness of fit, Kolmogorov-Smirnov test-Exercises Week 13. Correlation, Regression Analysis Recommended Reading: Α) Principal Reference: [Option 1] Εισαγωγή στη Στατιστική, Τ. Παπαϊωάννου, Σ .Β. Λουκάς, Εκδόσεις Σταμούλη Α.Ε., Κωδικός Βιβλίου στον Εύδοξο: 22745 (in greek) [Option 2] Πιθανότητες και Στατιστική για Μηχανικούς, Γ. Ζιούτας,, Εκδόσεις "σοφία" Ανώνυμη Εκδοτική & Εμπορική Εταιρεία, Κωδικός Βιβλίου στον Εύδοξο: 12656654 (in greek) Β) Additional References: 1. Εισαγωγή στις πιθανότητες και τη στατιστική, Δαμιανού Χ., Χαραλαμπίδης Χ., Παπαδάκης Ν., Εκδόσεις Συμμετρία, 2010 (in greek) 2. Πιθανότητες και Στατιστική, (Schaum's Outline of PROBABILITY AND STATISTICS), Murray R. Spiegel, Μετάφραση: Σωτήριος Κ. Περσίδης (in greek) 3. Στατιστική, Υ. Κολυβά-Μαχαίρα, Ε. Μπόρα-Σέντα, Ζήτη (in greek) 4. Ανάλυση Δεδομένων με τη Βοήθεια Στατιστικών Πακέτων SPSS, Excel, S-Plus, Ν. Δ. Σσάντας, Φρ. Θ. Μωϋσιάδης, Ντ. Μπαγιάτης, Θ. Φατζηπαντελής, Εκδόσεις Ζήτη, Θεσσαλονίκη 1999. (in greek) 5. Introductory Statistics, S M. Ross, Second Edition,, Academic Press; 2 edition, 2005 6. Theoretical statistics, D. R. Cox, D. V. Hinkley, London:Chapman and Hall, New York, 1979. 7. Statistics: An Introduction using R, M. J. Crawley, Wiley; 1 edition, 2005. 8. Introduction to probability and statistics: principles and applications for engineering and the computing sciences, J. S. Milton, Jesse C. Arnold, 3rd ed. New York :McGraw-Hill, 1995. 9. Introduction to statistical theory, Paul G. Hoel, Sidney C. Port, Charles J. Stone, Boston :Houghton-Mifflin, 1971. 10. An Introduction to Statistics, G. Woodbury, Duxbury Press; 1 edition, 2001) Teaching Methods: Statistical Inference theory, examples and exercises. Lab in SPSS Assessment Methods: Final Exams = 20% + Assignment is SPSS = 20% Language of Instruction: Greek Module Objective (preferably expressed in terms of learning outcomes and competences): The aim of the course consists in introducing the basic concepts of Statistical Inference. These concepts are prerequisites for future courses (Financial Econometrics, Forecasting and Applied Statistical Techniques) A successful student should be able to: understand and use basic statistical concepts underlying the characteristics of a population based on a random sample compute and interpret confidence intervals for estimations conduct hypothesis testing for the mean of a population, the binomial p, the difference between the means of two population, the variance of a population comprehend “non-parametric statistic” and conduct the appropriate tests use linear regression to examine the relation between an independent and a dependent variable, along with interpreting the results of regression