Faculty of Economics and Business
BACHELOR IN ECONOMICS SECOND YEAR Course
Statistics II
Code
802354
Module
Quantitative Methods
Area
Statistics and Econometrics
Nature
Compulsory
Attendance
2.7
Non-attendance
3.3
Semester
3
Credits
6
Year
2
COORDINATION DEPARTMENT Department of Statistics and Operations Research II (Decision-Making Methods)
COORDINATOR AND CONTACT Roque Piñole Villar:
[email protected]
% OF TOTAL CREDITS
ATTENDANCE
Lectures
30%
100%
Classes
10%
50%
Tutorials
6%
100%
Assessment activities
4%
100%
Homeworks and class assignments
20%
0%
Time to study
30%
0%
TEACHING ACTIVITIES
SYNOPSIS 1
Faculty of Economics and Business
BRIEF DESCRIPTION The main aspects of Statistical Inference will be developed: probability distribution of relevant statistics, point estimation, confidence interval estimation and hypothesis tests.
PRE-REQUISITES Those corresponding to the courses Mathematics I, Mathematics II and Statistics I of the basic training programme of the degree.
OBJECTIVES Application of the parametric, inferential methods to extrapolate the sample information.
COMPETENCES General: CG1, CG2, CG3, CG4. Cross-sectional: CT1, CT2, CT3. Specific: CE5, CE7, CE8, CE9.
LEARNING METHODOLOGY A mixed teaching-learning methodology will be applied to all educational activities for the students’ learning to be collaborative and cooperative.
TOPICS COVERED (Syllabus) TOPIC 1: Introduction to Inference 1.1. Population and sample 1.2. Inferential methods TOPIC 2: Distribution of statistics 2.1. Simple random sampling. Statistics and sampling distributions. 2.2. Central limit theorem 2.3. Distributions related to the Normal distribution a) Chi-square 2 distribution b) Student’s t distribution c) Snedecor’s F distribution 2.4. Sampling distributions a) Distribution of the sample mean for a Normal population b) Distribution of the sample variance for a Normal population c) Distribution of the sample proportion d) Distribution of the difference of means for two Normal populations e) Distribution of the quotient of variances for two Normal populations f) Distribution of the difference of sample proportions TOPIC 3: Estimation of parameters
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Faculty of Economics and Business 3.1. Concept of estimator. Point estimation. Usual properties of point estimators 3.2. Obtaining estimators by the maximum likelihood method and the method of the moments 3.3. Interval estimation. Notion of confidence interval. Construction of confidence intervals; main cases TOPIC 4: Hypothesis testing 4.1. Statistical hypotheses. Types of hypothesis Consequences of the decision about a hypothesis. Type I and type II errors. Concept of critical region. Concept of p-value 4.2. Significance tests 4.3. Power function. Neyman-Pearson’s theorem
ASSESSMENT Exams
% Share of Final Grade
50%
% Share of Final Grade
30%
% Share of Final Grade
20%
Final exam
Other Activities Quizzes
Other Activities
Active participation in the lecture room and during the practicals ------------ 10% of the final grade Resolution of exercises and problems during the classes ---------------------- 10% of the final grade
EVALUATION CRITERIA 1. Final exam: 50% of the final grade 2. Two partial quizzes consisting in the resolution of cases or exercises similar to those proposed in the worksheets. The mean score is 30% of the final grade 3. Active participation in the lecture room: 10% of the final grade 4. Execution and presentation of individual or group works: 10% of the final grade “Continuous evaluation in extraordinary call: For the students who have taken the final exam in the ordinary call, have not passed the continuous assessment and have done any of its activities, the grade of the continuous assessment will be the final grade of the ordinary call.” “NOT SAT” ASSESSMENT a- ORDINARY CALL Students who do not sit the first partial quiz (a month and a half after the beginning of the period) and the next ones will be considered as “Not sat”. Otherwise, the student is considered as “Sat” and his or her final grade will be the result of the application of the weights established in this academic guide. b- EXTRAORDINARY CALL If the students DOES NOT SIT the exam established by the Academic Secretary, the student will be considered as NOT SAT, regardless of whether he or she had followed the continuous
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Faculty of Economics and Business evaluation or not. If the student sits the exam, his or her grade will be the result of the application of the weights established in this academic guide.
IMPORTANT NOTE For the final exam and the quizzes, it is permitted the use of only a nonprogrammable scientific calculator. Electronic translators are not permitted.
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Faculty of Economics and Business
TIMETABLE Week
Contents
Work inside the lecture room
1ª
Introduction to the course TOPIC 1: Introduction to Inference Population and sample. Inferential methods
Course presentation Theoretical exposition Resolution of exercises that help to understand the practical usefulness of the theoretical concepts
TOPIC 2: Distributions of statistics Simple random sampling. Statistics and sampling distributions. Central limit theorem 2ª
TOPIC 2: Distributions of statistics
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of the theoretical concepts
Quiz 1 Theoretical exposition Resolution of exercises that help to understand the practical usefulness of the theoretical concepts on sampling distribution of statistics
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of point estimators
Continuous probability models related to the Normal distribution Distribution of the sample mean for a Normal population Distribution of the sample variance for a Normal population Distribution of the sample proportion 3ª
TOPIC 2: Distributions of statistics Distribution of the difference of means for two Normal populations Distribution of the quotient of variances for two Normal populations Distribution of the difference of sample proportions
4ª
TOPIC 3: Estimation of parameters Properties of estimators
5
Faculty of Economics and Business
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of point estimators
Methods to obtain estimators
First partial quiz Theoretical exposition Resolution of exercises that help to understand the practical usefulness of point estimators
7ª
Practical classes
8ª
Practical classes
TOPIC 3: Estimation of parameters
Resolution of practical cases by using the spreadsheet of Excel in the computer room Resolution of practical cases by using the spreadsheet of Excel in the computer room Theoretical exposition Resolution of exercises that help to understand the practical usefulness of confidence intervals
5ª
TOPIC 3: Estimation of parameters Usual properties of estimators. Methods to obtain estimators
6ª
9ª
TOPIC 3: Estimation of parameters
Interval estimation. Notion of confidence interval. Construction of confidence Intervals; main cases: means, proportions, variances Semana 10ª
TOPIC 3: Estimation of parameters
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of confidence intervals
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of the consequences of the decision about a hypothesis
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of the consequences of the decision about a hypothesis
Interval estimation (continuation) 11ª
TOPIC 4: Hypothesis testing Types of hypothesis. Type I and type II errors. Concept of critical region. Concept of p-value. Significance tests: mean, variance, proportion, difference of means, difference of proportions, quotient of variances
12ª
TOPIC 4: Hypothesis testing Significance tests: mean, variance, proportion, difference of means, difference of
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Faculty of Economics and Business proportions, quotient of variances 13ª
TOPIC 4: Hypothesis testing Neyman-Pearson’s theorem
14ª
Practical classes
15ª
Practical classes
Theoretical exposition Resolution of exercises that help to understand the practical usefulness of the consequences of the decision about a hypothesis Second partial quiz Resolution of practical cases by using the spreadsheet of Excel in the computer room Resolution of practical cases by using the spreadsheet of Excel in the computer room
NOTES: Each lesson lasts two hours. For the practical classes, the teacher will split all students into Group 1 and Group 2. Final exam: according to the dates established by the Deanery. This schedule is illustrative, since festivities affect groups in a different way and hence can change the progress of the subject as well as the dates and the number of quizzes.
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Faculty of Economics and Business
RESOURCES BASIC BIBLIOGRAPHY - Newbold, P., W.L. Carlson and B. Thorne. Statistics for Business and Economics. Pearson, 2013 ( M311NEW ). - Levine, D.M., D. Stephan, T.C. Krehbiel, M.L. Berenson and M.L. Berenson. Statistics for Managers Using Microsoft Excel. Pearson-Prentice Hall, 2008 ( M311STA ). - Downing, D., and J. Clark. Business Statistics. Barron's, 2010. ( S519.22DOW )
OTHER RESOURCES - Materials available for the students through the Virtual Campus. - Important teaching information (card of the subject, schedule of tutorials, information about the practicals...) - Slides of the theoretical lectures - Proposed and supplementary exercises - Databases: INE, Eurostat and other official organizations - Other additional materials - Software: Spreadsheet Excel
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