School of Economics and Business

BACHELOR'S DEGREE IN BUSINESS ADMINISTRATION Course

Business Statistics II

Code

802280

Module

Cross-sectional formation

Area

Quantitative methods

Character

Compulsory

Attendance

2.7

Nonattendance

3.3

Semester

4

Credits

6

Year

Second

Department

Department of Statistics and Operations Research II (Decision-Making Methods) Coordinator: Enrique García Pérez

Professor

E-mail

David Casado de Lucas

[email protected]

SYNOPSIS BRIEF DESCRIPTION Study and application of methods of Statistical Inference: estimation of parameters and hypothesis tests.

RECOMMENDED PREREQUISITES Those corresponding to the courses: Business Mathematics I and II, and Business Statistics I.

OBJECTIVES OBJECTIVES (Learning Outcomes) Instrumental knowledge of Inferential Statistical methods as tools to both describe the economic environment and support decision making in business.

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COMPETENCES General: CG1, CG2 Cross-sectional: CT1, CT2, CT4 and CT5 Specific: CE3, CE4, CE5 and CE6

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)

Chapter 1: Probability models linked to the Normal distribution. 1.1. Gauss' Normal distribution: N(0;1) and N(μ;σ2). Review. 1.2. Pearson's “χ2” or chi-square distribution. 1.3. Student's “t” distribution. 1.4. Snedecor's “F” distribution. Chapter 2: Sampling. Sampling distribution of statistics. 2.1. Population. Notion of sample. Simple random sampling. Statistics: sample mean, sample proportion, sample variance and sample quasivariance. 2.2. Sampling distributions. 2.3. Sampling distribution of statistics under Normal populations. 2.4. Joint distribution of the sample: likelihood function. Main cases. Chapter 3: Point estimation of parameters. Properties. Methods to obtain estimators. 3.1. Concept of estimator. Mean square error of an estimator. 3.2. Biased and unbiased estimator. 3.3. Efficient estimator. Cramér-Rao’s bound. 3.4. Consistent estimator. 3.5. Maximum likelihood method. 3.6. Method of the moments. Chapter 4: Confidence intervals. 4.1. Concept of confidence interval. 4.2. Method to construct confidence intervals.

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4.3. Confidence intervals under Normal populations. 4.4. Confidence intervals under large samples. Chapter 5: Hypothesis tests. Main concepts. 5.1. Statistical hypotheses. Types. 5.2. Fundamental concepts. Consequences or errors. Critical region. Significance level. Power of the test. P-value. 5.3. Methods to construct hypothesis tests. Chapter 6: Significance parametric tests. 6.1. Basic scheme to construct a significance test. 6.2. Tests for the mean of a Normal population. 6.3. Tests for the variance of a Normal population. 6.4. Tests for the equality of variances of two Normal populations. 6.5. Tests for the equality of means of two Normal populations. 6.6. Tests for population proportions under large samples. 6.7. Introduction to ANOVA: tests for the equality of means of more than two Normal populations. 6.8. ANOVA: one-factor model. Chapter 7: Nonparametric tests. 7.1. χ2 goodness-of-fit test. 7.2. χ2 independence and homogeneity tests. 7.3. Kolmogorov-Smirnov goodness-of-fit test. 7.4. Runs tests. 7.5. Other nonparametric tests.

% OF TOTAL CREDITS

ATTENDANCE

Lectures

20%

100%

Classes

20%

75%

Tutorials

6%

100%

Assessment activities

4%

100%

Homeworks and class assignments

20%

0%

Time to study

30%

0%

TEACHING ACTIVITIES

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ASSESSMENT Exams

% share of final grade

60%

Final exam covering all topics included in the syllabus of the course. Other activities

% share of final grade

30%

Discussion of cases and exercises. There will be several quizzes along the semester. Works and exercises could be assigned as homework. Other activities

% share of final grade

10%

Active participation in the lecture room and during the practical activities, through the interventions in the classes: solving exercises, answering other questions or proposing doubts and discussions. ASSESSMENT CRITERIA For the ordinary call, the student will be allowed to make use of the “Not sat” grade if he or she stops attending the lectures or making the practical activities of the course within the first month and a half of teaching activity. From this point forward, he or she is supposed to be following the continuous assessment system to all intents and purposes. If a student does not sit the extraordinary call of the Academic Secretary, he or she will be considered as “Not sat”, regardless of whether he or she had followed the continuous evaluation or not. If the student sits the extraordinary call, his or her grade will be the result of the application of the weights established in this academic guide. 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.

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GUIDING TIMETABLE Week

Topic

1st

Presentation. Topic 1: Pearson’s “χ2”, Student’s “t” and • Snedecor’s “F” distributions.

Use of the statistical tables of the • “χ2”, “t” and “F” distributions.

Topic 2: Simple random sampling. Probability sampling • distributions. Distributions of statistics under Normal populations. • Topic 2: Distribution of statistics. Likelihood function. Topic 3: Concept of estimator. MSE of an estimator. • Properties: unbiased, efficient and consistent.

Exercises statistics.

2nd

3rd

4th

Work in the classroom

• Review of topics 1 and 2. •

5th

Topic 3: Maximum likelihood method. Method of the moments.

6th

Topic 4: Confidence intervals. Method of the pivot. • Cases under Normal populations. Topic 4: Confidence intervals. Method of the pivot. • Cases under large samples. • Review of topics 3 and 4.

7th 8th

on

distribution

Exercises on distribution statistics. Exercises of topic 3 (properties)

Work outside the classroom

of • of •

Practical Activity (2 hours): Practicals of topic 1, on the • generation of samples, and practicals of topic 2. Exercises of topic 3 (methods and • properties) Examples and exercises on • confidence intervals. Examples and exercises on • confidence intervals. Practical Activity (2 hours): • Practicals of topics 3 and 4.

Reading and study of the materials of topic 1. Resolution of proposed exercises. Reading and study of topic 2. Resolution of proposed exercises. Reading and study of topic 2. Resolution of proposed exercises. Reading of the materials of topic 3. Study of topic 3. Resolution of proposed exercises. Study of topic 3. Resolution of proposed exercises. Reading of the materials of topic 4. Study of topic 4. Resolution of proposed exercises. Study of topic 4. Resolution of proposed exercises. Reading of the materials of topic 5.

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Week

Topic

9th

Topic 5: Hypothesis tests. Fundamental concepts. • Beginning of topic 6: significance parametric tests.

10th

11th 12th 13th 14th

Topic 6: Significance parametric tests.

Topic 6: Significance parametric tests.

Review of topics 5 and 6.

Work in the classroom

•

Study of topic 5. Resolution of proposed exercises. Reading of the materials of topic 6.

Examples and exercises of topic 5

•

Exercises of topic 6.

•

Study of topic 6. Resolution of proposed exercises.

•

Exercises of topic 6.

•

Study of topic 6. Resolution of proposed exercises.

•

Practical Activity Practicals of topic 6.

hours): •

Study of topic 6. Resolution of proposed exercises. Study of topic 7. Resolution of proposed exercises.

Topic 7: Nonparametric tests: goodness-of-fit and • independence χ2 tests. Topic 7: Nonparametric tests: goodness-of-fit • Kolmogorov-Smirnov test. Runs test. Other •

nonparametric tests.

Work outside the classroom

(2

•

Exercises of topic 7. Exercises of topic 7. Practical Activity Practicals of topic 7.

(1

hour):

•

Study of topic 7. Resolution of proposed exercises.

School of Economics and Business

RESOURCES BASIC BIBLIOGRAPHY 1. Newbold, P., W.L. Carlson and B. Thorne. Statistics for Business and Economics. Pearson, 2013 ( M311NEW ). ADDITIONAL BIBLIOGRAPHY 2. Downing, D., and J. Clark. Business Statistics. Barron's, 2010. ( S519.22DOW ) 3. 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 ). OTHER RESOURCES Materials provided by the teachers of the course through the Virtual Campus. Software programme: Excel 2010.