Faculty of Economics and Business

BACHELOR IN ECONOMICS SECOND YEAR Course

Statistics II

Code

802354

Module

Quantitative Methods

Area

Statistics and Econometrics

Nature

Compulsory

Credits

Attendance

3

6

Non attendance

3

Year

2

Semester

3

COORDINATION DEPARTMENT Estadística e Investigación Operativa II

COORDINATOR AND CONTACT Blanca de la Fuente; [email protected]

SYNOPSIS 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 Obtain probability models which could allow us to explain the behaviour of economic phenomena. Methods to project the sample information with both parametric and nonparametric inference approaches.

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COMPETENCES General: CG1, CG2, CG3, CG4. Transversal: CT1, CT2, CT3. Specific: CE5, CE7, CE8, CE9.

LEARNING METHODOLOGY A mixed methodology of teaching and learning will be used in all educational activities with the aim of encouraging students to develop a collaborative and cooperative attitude in the pursuit of knowledge.

TOPICS COVERED (Syllabus) TOPIC 1: Inferential methods 1.1. Sequences of random variables and theorems of convergence. Central Limit Theorem. De Moivre's theorem. 1.2. Sampling and statistic 1.3. Sampling distributions: Distribution of the sample mean. Distribution of the sample proportion. Distribution of the sample variance. Distribution of the difference of sample means and sample proportions. Distribution of the quotient of sample variances. TOPIC 2: Parameter estimation 2.1. Concept of estimator. Point estimation. Basic properties of point estimators. 2.2. Construction of estimators by applying the Maximum Likelihood Method or the Method of the Moments. 2.3. Interval estimation. The concept of confidence interval. Construction of confidence intervals; main cases. TOPIC 3: Testing hypotheses 3.1. Statistical hypotheses. Types of hypothesis. Consequences of making a decision about a hypothesis. Type I and type II errors. Concept of critical region. Concept of p-value. 3.2. Tests of significance. 3.3. Power function. Neyman-Pearson theorem. TOPIC 4: Nonparametric tests 4.1. Independence tests. 4.2. Goodness-of-fit tests. χ2 tests. 4.3. Kolmogorov-Smirnov tests.

TEACHING ACTIVITIES DISTRIBUTION Theoretical lessons

% of Total Credits

25%

In the lesson previous to that where theoretical concepts will be introduced, students are given some advice for them to prepare the topic and hence to be able to participate. In the classroom,

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the topic will be presented by using auxiliary PowerPoint outlines. During the explanations, the students will be required to participate and argue about the concepts presented. That previous preparation of the topic will qualify the students to do some proofs or to answer the questions.

Practical lessons

% of Total Credits

10%

Discussion of practical cases using appropriate statistical software (seminars).

Other Activities

% of Total Credits

15%

Personalized & Group Tutoring; Assessment Activities

Other Activities

% of Total Credits

50%

Individual & Group Homework Assignments; Hours to Study

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 classroom and in the seminars -------------------- 10% of the final grade Solution of practical exercises and problems in the classroom --- ---------- 10% of the final grade

EVALUATION CRITERIA 1. Final exam: 50 % 2. Two partial quizzes based on cases or exercises similar to those proposed in worksheets: 30% 3. Active participation in classroom and seminars: 10% 4. Individual/group projects (with oral presentations): 10% “Not sat” assessment a- REGULAR CALL Students will be considered “Not sat” if they DO NOT SIT the first partial quizz (around the first month and a half) and the next ones. Otherwise, they are supposed –to all intents and purposes– to be following the continuous assessment system, and their grade will be the result of the application of the weights above-mentioned in this academic guide. b- EXTRA CALL If students DO NOT TAKE the exam established by the Academic Secretary, they are considered NON-TAKEN, regardless of whether or not they had been following the continuous

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evaluation. If students take the exam, their final grade will be the result of applying the percentages published in the academic guide of the subject.

IMPORTANT NOTE For both the final exam and the tests, only the use of a nonprogrammable scientific calculator is permitted. Electronic translators are not permitted.

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Faculty of Economics and Business

TIMETABLE Week

Contents

Work inside the classroom

1ª

TOPIC 1: Introduction to the course

• PresenPresentation of the subject. • Sequences of random variables and convergence theorems: Central Limit Theorem. De Moivre's theorem • Solution of exercises to help understanding the practical usefulness of the theoretical conceps. • Continuous probability models linked to the normal distribution: Chi-square, t-Student, F-Snedecor • Solution of exercises to help understanding the practical usefulness of the theoretical concepts. • Sampling and statistics

Inference methods 1.1Sequences of random variables and convergence theorems

2ª

TOPIC 1: Inference methods Continuous probability models linked to the normal distribution 1.2 Concept of sample. Types of samples. Concept of statistic.

3ª

4ª

TOPIC 1: Inference methods 1.3 Sampling distributions. Distribution of some statistics: simple mean, simple proportion, simple variante, mean difference a and proportion difference Distribution of ratio of variances TOPIC 1: Inference methods 1.3 Sampling distributions (continuation). Distribution of some statistics: difference of means and proportions, and quotient of variances

Work outside the classroom

1. Study of Topic 1 (1.1) 2. Exercises in worksheets

• •

Study of Topic 1 (1.1 and 1.2) Exercises in worksheets

• Exercises on the distribution of statistics • Solution of exercises to help understanding the practical usefulness of the theoretical concepts.

• Study of topic 1 (1.3) • Proposed exercises in worksheets

• Solution of exercises to help understanding the practical usefulness of the theoretical concepts on the distribution of the statistics • Seminar 1 (2 hours, with group 1): solution of practical cases by using spreadsheet Excel cases.

• •

Study of topic 1 Proposed exercises in worksheets

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5ª

6ª

7ª

TOPIC 2: Parameter estimation 2.1 Concept of estimator. Point estimation. Properties of estimators TOPIC 2: Parameter estimation 2.1 Basic properties of estimators (continuation).

• •

TOPIC 2: Parameter estimation 2.2 Methods to obtain estimators: Maximum Likelihood Method. Method of the moments

• Examples of point estimators • Study of Topic 2 (2.1 and 2.2) • Seminar 2 (2 hours, with group 2): solution of 4. Exercises in worksheet practical cases by using spreadsheet Excel cases

Examples of point estimators Seminar 1 (2 hours, with group 2): solution of practical cases by using spreadsheet Excel cases. • Examples of point estimators • Seminar 2 (2 hours, with group 1): solution of practical cases by using spreadsheet Excel cases.

• Study of Topic 2 (2.1) 3. Exercises in worksheet • •

Study of Topic 2 (2.1) Proposed exercises in worksheets

Interval estimation. Concept of confidence interval. 8ª

TOPIC 2: Parameter estimation 2.2 Methods to obtain estimators: Maximum Likelihood Method. Method of the Moments (continuation).

• Examples of point estimators

• Study of Topic 2 (2.1 and 2.2) 5. Exercises in worksheet

9ª

TOPIC 2: Parameter estimation 2.3 Obtaining confidence intervals. Main cases: mean, proportion, variance. (continuation).

• Partial quiz I: Topic 1 (I, II, III) and topic 2.1 and 2.2 • Examples of confidence intervals

• Study of Topic 2 (2.3) 6. Exercises in worksheet

. 10ª

TOPIC 2: Parameter estimation • Examples of confidence intervals 2.3 Obtaining confidence intervals. Main cases: difference of means, difference of proportions, quotient • Seminar 3 (2 hours, with of variances. group 1): solution of practical cases by using spreadsheet Excel cases

7. Exercises in worksheet

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Faculty of Economics and Business

11ª

12ª

TOPIC 3: Hypothesis tests • Examples of consequences of making a 3.1 Types of statistical hypotheses. Type I and type II errors. Critical decision about a hypothesis or rejection region. Concept of p-value • Seminar 3 (2 hours, with group 2): solution of practical cases by using spreadsheet Excel cases TOPIC 3: Hypothesis tests • Examples of Hypothesis tests 3.2 Significance tests: mean, proportion, variance, difference of • Seminar 4 (2 hours, with group 1): solution means, difference of proportions, quotient of variances. of practical cases by using the spreadsheet Excel

• Study of Topic 3(3.1) 8. Exercises in worksheet

• Study of Topic 3 (3.1 and 3.2) 9. Exercises in worksheet

13ª

TOPIC 3: Hypothesis tests 3.3 Theorem of Neyman-Pearson. Power function. Uniformly most powerful tests

• •

14ª

TOPIC 4: Nonparametric tests • Independence tests. Goodness-of-fit tests. 2 • χ tests.

• Partial quiz II: Topic 2 , topic 3 • Examples of nonparametric tests

11. Study of Topic 4 (4.1 and 4.2) 12. Exercises in worksheet

15ª

TOPIC 4: Nonparametric tests (continuation) 4.3 Kolmogorov-Smirnov tests.

• Examples of nonparametric tests Review of topics

13. Study of Topic 4 14. Exercises in worksheet

Examples of Theorem of Neyman-Pearson 1. Study of Topic 3 Seminar 4 (2 hours, with group 2): solution 10. Exercises in worksheet of practical cases by using spreadsheet Excel cases

NOTE: Each lesson takes two hours. For the seminars, the teacher will split all students into Group 1 and Group 2. Final exam: according to the schedule established by the Deanery.

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Faculty of Economics and Business The schedule above is approximate, since nonworking days affect groups in a different way, which can change the progress of the subject, the dates and even the number of quizzes.

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Faculty of Economics and Business

RESOURCES BASIC BIBLIOGRAPHY - Levine, D.M. "Statistics for Managers Using Excel", International Edition, 5/E, Pearson Higher Education - Newbold, P., Carlson, W.L. and Thorne, B. "Statistics for Business and Economics", International Edition, 7/E, 2009, Edit. Pearson Higher Education

OTHER RESOURCES - Materials for the module will be available through the Campus Virtual. - Important teaching information (card of the subject, tutorship schedule, information about seminars...) - 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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