Mathematical-statistical analysis of experimental work on the use of modeling programs for future engineers

. Through this article, you can get information about the methods implemented on the basis of training using programs for modeling the teaching process in the general professional subject "Technical applications on the basis of programming languages" and see the statistical analytical results of the effectiveness of the experimental tests conducted in order to determine the effectiveness of training using the programs.


Introduction
In order to determine the effectiveness of the results obtained in conducting experimental work, the results obtained in two parallel experimental and control groups from higher education institutions were compared with each other in the assessment of students' professional knowledge and skills.In the control groups, the teaching process was carried out on the basis of traditional teaching, while in the experimental groups, the e-learning offered by us was conducted on the basis of distance learning using the resource [1].The results of the control and experimental groups at the beginning and at the end of the experiment were systematically analyzed and compared to each other and summarized.The effectiveness of the use of electronic educational resources in the experimental group was proved on a theoretical basis and practically.
We have observed an increase in educational efficiency in teaching as a result of organizing the teaching process of the general professional subject "Technical applications based on programming languages" on the basis of electronic educational resources.For this purpose, for 2 years, we conducted research and monitoring work in control and experimental-testing groups at Bukhara Engineering-Technological Institute of Bukhara Region, Namangan Engineering-Technological Institute of Namangan Region, Fergana Polytechnic Institute and Jizzakh Polytechnic Institute of Jizzakh Region [2].
A total of 482 students participated in the experimental and control groups.Among them, 110 people (out of 52 in the experimental and control groups) in Bukhara Engineering-Technological Institute, 160 people in the Namangan Engineering-Technological Institute (out of 80 in the experimental and control groups), 105 people in Fergana Polytechnic Institute (52 in the experimental groups and in the control groups) 53 students) and 107 (53 experimental and 54 control group) students participated in Jizzakh Polytechnic Institute [3].Technical applications on the basis of programming languages" in general professional subject using modeling programs was taught by teachers of general professional subjects of higher education institutions;  drawing scientific conclusions, scientific justification of the research results, their compatibility with the hypotheses and tasks, i.e. their suitability [5];  opinions of the teachers of professional subjects who participated in the experimental work were studied, interviews and questionnaires were conducted in order to make sure that the quality and efficiency of the educational process increased;  statistical processing of all the materials collected during our research, to prove its reliability, and mass promotion of our methodical work in practice.
In order to conduct experimental work and ensure the objectivity of the results, two parallel groups were gradually designated as experimental and control group in each academic year.In the control groups, the educational process was carried out according to the current teaching methodology, while in the experimental groups, it was carried out on the basis of training using modeling programs of the educational process in the general professional subject "Technical applications on the basis of programming languages" offered by us.
The results of the control and experimental groups were systematically analyzed and compared to each other, and a conclusion was drawn.In necessary cases, opinions expressed by teachers directly participating in this process were thoroughly discussed.For this purpose, we conducted research and observation work in control and experimental groups for 2 years [6].

Fig. 2. Scheme of the program for modeling the teaching process
We performed mathematical and statistical processing to ensure the validity of the experimental results.Based on the author's methodology, the high level of teaching the subject "Technical applications on the basis of programming languages" using modeling programs was confirmed by the results of experimental work -it can be seen that excellent grades increased from 10.1% to 30.8% in the period from 2022 to 2023.In this case, students were evaluated on the basis of appropriate criteria in the course of the test conducted on the example of the subject "Technical applications on the basis of programming languages".

Criteria for evaluating the use of student modeling programs in the process of test-verification work on the subject "Technical applications on the basis of programming languages"
HIGH -in addition to the criteria specified at the intermediate level.Data  understanding of the Delphi visual model.Not knowing the basics of object-oriented programming [8].
Based on these indicators, an experiment was conducted on the results of a test to determine the effectiveness of teaching students the subject "Technical applications based on programming languages" using modeling programs based on the author's methodology, and their average assimilation in the control group was analyzed using the χ2 mathematicsstatistics method according to Student and Pearson.
The brief essence of the problem is as follows: Let two prime sets be given.One is the mean scores of the students in the experimental group and the other is the mean scores of the students in the control group.The scores are assumed to have a normal distribution.This assumption is reasonable because the conditions for approximation to the normal distribution are simple and they are satisfied.
Based on the above tables, we choose hypothesis Н1, which shows the effectiveness of students' learning in the experimental group and in the control group, and the hypothesis Н0, which contradicts it.
We can determine the mastery rates and the number of students in the experimental group and the control group by means of хi, and yi, respectively.хi -values corresponding to the experimental group.i = 3 , 1 yi -values corresponding to the control group.
x and y -formulas of arithmetic mean values corresponding to the experimental and control groups.
Here: xi, yi -accepts values of 3, 4, 5, respectively.n, m -the number of students in the experimental and control groups.ni , mi, -the number of students in relation to the corresponding grades.
The average value that evaluates the effectiveness of the educational process is the ratio of the average arithmetic values of the experimental and control groups, that is, the efficiency coefficient was obtained as follows: Mean square deviation values: Standard deviation values: Indicator for determining average values: Confidence intervals for unknown population means: Here t is the normalized deviation confidence probability Р is determined.In this case, Р =0.95 equals t=1.96.
We put forward the hypothesis H0:ax=ay about the equality of mean values, and check its opposite H1:axay based on the above data using Student's statistics.We carried out mathematical calculations at each stage.Now, according to these results, we check and draw conclusions using the above formula 7 from Stoudent statistics.It can be seen that the sampling value of the statistic is greater than the critical point: Tm=8,34  T0,96=t=1,96 hence, the Н0 zero hypothesis about the equality of Prime mean values is rejected.This can be said with 95% reliability that the average acquisition rates in experimental groups have always been higher than the average acquisition rates in control groups, and they will never fall above them.Hence, the Н0 hypothesis is rejected and the Н1 hypothesis is accepted.
Control group:  ̅ б = 3,35 and  ̅ о = 3,54  So, the statistical analysis of the effectiveness of experimental studies conducted to determine the effectiveness of students in teaching the subject "Technical applications on the basis of programming languages" using modeling programs based on the author's methodology revealed that at the end of the experimental studies in all higher education institutions, the knowledge level of the students of the experimental group was higher than that of the control group compared to 1.15 (15%) had a higher rate.This shows that the conducted research work is effective [11][12][13].

Fig. 1 . 3 .
Fig. 1.Scheme of efficiency of use of e-learning resources The purpose of pedagogical experiments is to prove the correctness of the hypothesis put forward in scientific research work.This process can be conditionally divided into the following stages: 1.The preparatory stage was held during 2020-2021, during which the following activities were carried out:  determining the main direction of research;  study the theoretical and practical situation of the problem;  selection of higher education institutions, study of material-technical, scientificmethodical basis and pedagogical conditions for conducting experimental work in them;  preparation of materials necessary for experimental work;  conducting preliminary experimental work, etc [4].2. At the second stage -2021-2022, the following was implemented:  continue experimental work according to the plan;  conducting a survey of teachers and students of general professional disciplines of higher educational institutions;  preparation of teachers of general professional subjects working in higher educational institutions to conduct experimental work;  making changes to the content of experimental materials and the methodology for their implementation, if necessary;  quantitative and qualitative analysis of the results of experiments;  collection of scientific data, their generalization;  presentation of reports on the results of experimental work and their detailed discussion.3. The third stage of research -in 2022-2023:  experimental work was continued;  A 72-hour training course on the development of "Technical applications on the basis of programming languages" in general professional subject using modeling programs was taught by teachers of general professional subjects of higher education institutions; drawing scientific conclusions, scientific justification of the research results, their compatibility with the hypotheses and tasks, i.e. their suitability[5]; Conferences 458, 06008 (2023) EMMFT-2023 https://doi.org/10.1051/e3sconf/202345806008

Table 1 .
Bukhara Engineering-Technological Institute, the results of the experimental tests conducted on student learning indicators in 2022-2023

Table 2 .
Namangan Engineering-Technological Institute, the results of the experimental tests conducted on student learning indicators in 2022-2023

Table 3 .
Fergana Polytechnic Institute, the results of the experimental tests conducted on student learning indicators in 2022-2023

Table 4 .
Jizzakh Polytechnic Institute, the results of the experimental tests conducted on student learning indicators in 2022-2023 input and output to the computer.Management of equipment for data collection.Using local, global and network variables.Event driven programming.Structures for removing codes.Polymorphism in virtual machines.Create internal virtual machines.Dynamic Link Libraries [7].Working with streams.Knowledge and experience with technologies such as OLE df Active X controls and buffering is required.INTERMEDIATE -a lower level, except for the specified criteria.There are two types of loops in LabVIEW.Shift registers.Option structure.Arrays.Clusters.LabVIEW visualization tools.Working with additional components.Must have knowledge, skills and experience in database linking and reporting applications.LOWER -Introduction to the LabVIEW environment.Creation of virtual hardware.Connecting elements.Program firmware.Download and save virtual hardware.Visual model of Delphi.Working with components.Availability of knowledge, skills and experience in creating work applications.LOW -Lack of familiarity with the LabVIEW environment.Not knowing how to connect fundamental concepts and elements in the LabVIEW environment.Lack of Efficiency coefficient.н = 1,38Tн=1,38  1,96 бўлиб, Н0 hypothesis is accepted.

Table 5 .
[10]rical data calculated based on the above formulas are presented in table[10].