AN EXAMPLE OF CONSTRUCTING A THEORETICAL DISTRIBUTION LAW BASED ON EMPIRICAL DATA FOR PRACTICAL CLASSES IN PROBABILITY THEORY

Abstract

The article is devoted to the methodology of teaching an important section of the probability theory course, namely, the construction and testing of statistical hypotheses. The article considers the possibilities of applying stochastic methods to problems related to electoral research, which is relevant in the process of teaching a course on probability theory to students of sociology. Mastering the methods of this discipline allows you to build models of stochastic processes and phenomena and analyze them. On the basis of quantitative surveys and questionnaires, students should learn how to determine the sample size, i.e., how many people should be interviewed to draw correct conclusions from their answers, as well as how to process and analyze the collected statistical data. The article presents an example of a survey conducted among students of the Faculty of Sociology and Law of the National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» and the processing of its results. Students were suggested to generate empirical data by questioning their colleagues. The task was to collect ratings of the five most popular parties at that time. Thus, the political views of students on the eve of the election were studied, namely, the task was to evaluate the proposed five parties in points, to highlight those they liked the most and least. To analyze the results of the survey, a random variable is introduced – the number of respondents who gave the maximum score to a particular party, and a distribution is also considered where the random variable is the number of respondents who gave the minimum score to a particular party, i.e. the number of those who gave a particular party the maximum score – five, and the minimum score – one. For these distributions, the hypotheses that they belong to the binomial and Poisson distributions are tested using the Pearson chi-square test. These distributions are closely related to the normal distribution of the population, which is the basis for many criteria. This example demonstrates that it is not enough to rely only on the graphical interpretation of the distribution, even when the graphs of the empirical and theoretical distributions are virtually identical.