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Mathematical Statistics

Course developer

Course abstract

Students acquire widely used mathematical statistics techniques for analysis of business, economic and socio-demographic processes. Students learn theoretical distributions and their trait; students achieve a competence of an evaluation of statistical parameters and hypothesis testing, an investigation with methods of mathematical statistics in economics, data collecting and an interpretation of results.

Learning outcomes and their assessment

Knowledge:
• knowledge of nature and concepts of mathematical statistics — Examination;
• knowledge and critical understanding of methods and relationships of mathematical statistics – independent studies;
• knowledge and critical understanding of the practical application of mathematical statistical techniques in business, in the analysis of economic and socio-demographic processes - test;
Skills:
• choosing and using mathematical statistical techniques relevant to observation data, - laboratory works;
• applying appropriate methods of mathematical statistics, performing a professional assessment of intermediate and final results and an interpretation in the analysis of business, economic and socio-demographic processes, test;
• to perform the necessary operations to process statistical data, using an appropriate software, - laboratory work and independent studies;
• planning and organizing self-study process, - independent studies;
Competence:
• in choosing mathematical statistical methods, to produce and interpret the results of the calculations and using them for statistically based decisions when dealing with business problems, economic and socio-demographic processes, - Examination.

Course Content(Calendar)

1. The nature and role of the course of mathematical statistics in studying economic processes, collecting, processing, analyzing and interpreting the results of economic studies. (lecture – 1 hour)
2. The probability distribution. (lecture– 1 hour, practice – 1 hour)
3. The probability distribution for a discrete random variable. Binomial distribution. Poisson distribution. Binomial distribution and Poisson distribution for solving business problems. (lecture– 1 hour, practice – 2 hours)
4. Continuous random variable. The Normal distribution and other continuous distributions. Probability density function. Standardized normal random variable. The Normal distribution in economics. (lecture– 2 hours, practice – 1 hour)
5. The basic principles of hypothesis testing. The assumptions of each hypothesis-testing procedure. Statistical conclusions. Level of significance. Region of non-rejection, region of rejection. Hypothesis testing methods. (lecture– 2 hours)
6. Parametric and non-parametric methods. (lecture– 1 hour)
7. Hypothesis testing for mean. Confidence interval. T statistics. P-value method. (lecture– 1 hour, practice – 2 hours)
Test. The probability distributions and their use in economic studies. (1 hour)
8. Hypothesis testing for variance. (lecture– 1 hour, practice – 1 hour)
9. Two-Sample Tests. The means of two independent populations. The means of two related populations. Comparing the Means. The proportions of two independent populations. The variances of two independent populations. F-test for the ratio of two variances. Interpretation of results in economic studies. (lecture– 3 hours, practice – 2 hours)
10. Chi-square test for the difference between two proportions. Chi-square test of independence. Interpretation of results in economic studies. (lecture– 1 hour, practice – 2 hours)
11. Analysis of variance. The basic concepts of experimental design. One-way analysis of variance for differences among the means of several groups. Two-way analysis of variance and the interaction effect. Interpretation of results in economic studies. (lecture– 2 hour, practice – 3 hours)
Test. Hypothesis testing methods and their use in economic studies. (1 hour)

Requirements for awarding credit points

Examination

The assessment of the examination depends on the cumulative assessment of the semester:
• co-evaluation of written tests;
• theory test (in writing).

Description of the organization and tasks of students’ independent work

The student has to prepare independently for tests, theory testing, and examination, according to the topics indicated in the curriculum of the course (see the course plan). Tasks for the independent work are included in e-studies every week.

Criteria for Evaluating Learning Outcomes

The assessment of the examination depends on the cumulative assessment of the semester:
•co-evaluation of practical tests (60 points as maximum);
• theory test (40 points as maximum).
Every 10 points make 1 examination mark.
One option is given to write a test.

Compulsory reading

1. Arhipova I., Bāliņa S. Statistika ekonomikā un biznesā. Rīga: Datorzinību Centrs, 2006. 364 lpp.
2. Arhipova I., Bāliņa S. Statistika ekonomikā. Risinājumi ar SPSS un Microsoft Excel. Rīga: Datorzinību Centrs, 2003. 352 lpp.
3. Arhipova I., Bāliņa S. Statistika ar MS Excel ikvienam. 1. daļa Rīga: Datorzinību Centrs, 1999. 163 lpp.
4. Arhipova I., Ramute L., Paura L. Datu statistiskā apstrāde ar MS Excel. Jelgava: LLU izdevniecība, 1998. 159 lpp.
5. Arhipova I., Ramute L., Žuka L. Matemātiskās statistikas uzdevumu risināšana ar MS Excel. I Jelgava: LLU izdevniecība, 1997. 121 lpp.
6. Arhipova I., Ramute L., Žuka L. Matemātiskās statistikas uzdevumu risināšana ar MS Excel. II Jelgava: LLU izdevniecība. 1997. 98 lpp.
7. Grīnglazs L., Kopitovs J. Matemātiskā statistika: ar datoru lietojuma paraugiem uzdevumu risināšanai. Rīga: Rīgas Starptautiskās ekonomikas un biznesa administrācijas augstskola, 2003. 310 lpp.
8. Krastiņš O. Ciemiņa I. Matemātiskā statistika. Rīga: LR Centrālā statistikas pārvalde, 2003. 267 lpp.
9. Krastiņš O. Statistika un ekonometrija. Rīga: LR Centrālā statistikas pārvalde, 1998. 436 lpp.
10. Koliškins A. Augstākā matemātika. Varbūtību teorija un matemātiskā statistika. III Rīga: Apgāds Zvaigzne ABC, 2011. 86 lpp.
11. Smotrovs J. Varbūtību teorija un matemātiskā statistika. I Rīga: Zvaigzne ABC, 2004. 264 lpp.
12. Smotrovs J. Varbūtību teorija un matemātiskā statistika. II Rīga: Zvaigzne ABC, 2007. 136 lpp.
13. Berenson M. L., Levine D. M. Basic Business Statistics. Concepts and Applications. USA: Prentice Hall, 2003. 1013 pp.
14. Graham A. Statistics: An Introduction. United Kingdom: Teach Yourself Books, 2017. 301 p.

Further reading

1. Revina I. Ekonometrija. Rīga: LU, 2002. 270 lpp.
2. Rowntree D. Statistics without Tears: An Introduction for Non-Mathematicians. United Kingdom: Penguin Books, 2018. 199p.
3. Cristensen R. Analysis of variance: design and regression. Applied statistical methods. London, UK: Published by Chapman & Hall. 1996. 587 pp.
4. Hair J. F., Anderson R. E., Tatham R. L., Black W. C. Multivariate data analysis with Readings. Fourth Editon. Prentice Hall, 1995.745 p.
5. McClave J.T., Benson P.G., Sincich T.A. First Course in Business Statistics. New Jersey: Prentice Hall, Inc., 1995. 746 p.
6. Freedman D., Pisani R., Purves R., Adhikari A. Statistics. 2nd ed. New York; London: W.W.Norton and Co., 1991. 514p.

Periodicals and other sources

1. Centrālās statistikas pārvalde: https://www.csb.gov.lv
2. EUROSTAT datu bāzes un publikācijas: https://ec.europa.eu/eurostat/

Notes

Compulsory course for Bachelor’s study programme “Economics” and field theoretical basic course for the second level professional higher educational programme “Entrepreneurship and Business Management”