In this assignment we will discuss the application of statistics and probability theory to a real world problem. The discussed topic is unethical behavior of business students at Rocky University. The problems of global financial crisis of 2008-2009 have demonstrated many cases of unethical behavior of financial managers, Wall Street executives and other corporate stuff. It was assumed that the reasons of such behavior may stem from the fact that cheating is the one of major problems among business students. The researchers reported a very high percentage of cheaters among business students compared to non-business students: approximately 86% of business students cheated at some time during their study, compared to 77% of other (non-business) students.
Among the problems of the modern education system, we can denote the decrease in the quality of education, lack of works originality, various manifestations of deception and dishonesty in the educational activity. The development of modern information technologies allows students to apply the method of writing that called “copy-paste” - copy material from the Internet with a minimum of editing. Such work can be also called as plagiarism. There are ,amu opposing views on plagiarism and other forms of misconduct in science: from outright rejection to the approval and support. Reflecting on the causes of the spread of plagiarism, the experts concluded that the problem originates during college education. Modern students are not taught to work with the text, they get the information from the Internet and thoughtlessly use it without analyzing. As a consequence, to the moment of entering university, they know nothing about information usage culture. They have no proper skills of the referencing to literature, when working with borrowed ideas. The problem of academic dishonesty and plagiarism in the spread of student works is very urgent and requires a comprehensive review (Uow.edu.au, 2016).
For several years, cheating was a real problem of the business faculties at Rocky University. However, there is no unified opinion about the seriousness of this problem: one faculty members believe that cheating is not the first problem of the college students; others think that cheating is more widespread at Rocky than in other universities. In order to examine this issue, a research study was conducted. An anonymous survey has been performed among a random sample of 90 graduate students from business faculties. The goal of this assignment is to consider the data, properly describe it and report the corresponding statistical inference.
In this paper, we will use such statistical techniques as descriptive statistics, proportions, confidence intervals for proportions, hypothesis tests and others. The paper will be summarized and recommendations will be given in the conclusion section.
Data Description and Methodology
As it was mentioned in introduction, an anonymous survey has been performed among a random sample of 90 graduate students from business faculties. This survey included the following three questions:
During your time at Rocky, did you ever present work copied off the internet as your own? (Yes / No).
During your time at Rocky, did you ever copy answers off another student’s exam? (Yes / No).
During your time at Rocky, did you ever collaborate with other students on projects that were supposed to be completed individually? (Yes / No).
Each answer was recorded and coded in the following variables: Copied from Internet, Copied on Exam, Collaborated on Individual Project (No was coded as “0”, Yes was coded as “1”). Also, the researchers have recorded respondents’ gender.
In this task we will calculate the proportion of all students, the proportion of all female students and the proportion of all male students who:
Collaborated with other students on projects that were supposed to be completed individually
Copied answers off another student’s exam
Presented work copied off the Internet as their own
The following 95% confidence intervals will be provided:
For proportions of students (by gender and together) that were involved in some type of cheating.
For proportions of students (by gender and together) that were involved in copying off the internet.
For proportions of students (by gender and together) that were involved in copying off another's exam.
For proportions of students (by gender and together) that were involved in collaborating on an individual project.
As a final step of the research, we will conduct a statistical test to examine the proportion of those who were not involved in any type of cheating, comparing it to the national average level for business students.
Data Analysis and Results
All calculations were performed in Excel. The first step of the assignment is to calculate the proportions of all students (and separately by gender) who were involved in any type of cheating (Stattrek.com, 2016). The results are given in the table below:
There were 44 male students and 46 female students who were involved in exit anonymous survey. 81 students (or 90%) were involved in some type of cheating during their time at Rocky University. Of those, 40 were males (90.91% of males) and 41 were females (89.13% of females). 42 students were involved in copying from Internet (46.67% of all students in the sample): 24 males (54.55% of males) and 18 females (39.13% of females). 48 students replied that they copied on exam (53.33%): 24 of them were males (54.55%) and 24 were females (52.17%). 45 students were involved in collaborating with mates on individual project (50%): 19 were males (43.18%) and 26 were females (56.52%).
The next step was to develop 95% confidence intervals for various type of cheating of all students (and also separately by gender). Developed intervals are presented in the tables below (Stattrek.com, 2016):
We are 95% confident that the true population proportion of all students who were involved in any type of cheating is between 0.838 and 0.962. We are 95% confident that the true population proportion of all students who were involved in copying from Internet is between 0.3636 and 0.5697. We are 95% confident that the true population proportion of all students who were involved in copying on exam is between 0.4303 and 0.6364. We are 95% confident that the true population proportion of all students who were involved collaborating on individual project is between 0.3967 and 0.6033. The similar interpretation may be given for confidence intervals of male and female students separately.
The final step of this research paper is to conduct a statistical test to examine the significance of the difference between the proportion of all business students at Rocky University who were not involved in any kind of cheating and the proportion of cheating business students elsewhere. We conduct all formal steps of the hypothesis testing (Stattrek.com, 2016):
Null hypothesis: The population proportion of all business students who were not involved in any kind of cheating at Rocky University is not significantly different from 14%.
Alternative hypothesis: The population proportion of all business students who were not involved in any kind of cheating at Rocky University is significantly less than 14%.
Set level of significance alpha = 0.05
Use z-test for difference between two population proportions (Statisticslectures.com, 2016):
Here, p is the sample proportion of all students who were not involved in any kind of cheating at Rocky University, p0 is the national average proportion (0.14).
The proportion of those who were not involved in any kind of cheating at Rocky is:
The corresponding p-value is 0.137. Hence, the null hypothesis is not rejected.
In this research work we have examined the proportions of male and female students, who were involved in such types of cheating as copying from internet, copying on exam and collaborating with mates on individual projects. It is appeared that the proportion of students that were involved in any kind of cheating is approximately equal between both genders. However, male students are more likely to copy from internet than females, but females collaborate with mates on individual projects more often than males. Both male and female students are equally likely to copy on exam.
As it was determined, the proportion of all students who were not involved in any kind of cheating at Rocky University is not significantly less than the national average of 14%. Hence, the problem of cheating is not the major problem of business faculties at Rocky University. However, the percentage of cheaters remains high for all kinds of cheating. I recommend all universities to put more attention about this issue, because this is one of the major problems of national education.
Statisticslectures.com,. (2016). One Sample z-Test for Proportions. Retrieved 7 February 2016, from http://www.statisticslectures.com/topics/onesamplezproportions/
Stattrek.com,. (2016). Proportion: Confidence Interval. Retrieved 7 February 2016, from http://stattrek.com/estimation/confidence-interval-proportion.aspx?Tutorial=AP
Stattrek.com,. (2016). Hypothesis Tests. Retrieved 12 February 2016, from http://stattrek.com/hypothesis-test/hypothesis-testing.aspx
Stattrek.com,. (2016). Means and Proportions. Retrieved 12 February 2016, from http://stattrek.com/sampling/central-tendency.aspx?Tutorial=Stat
Uow.edu.au,. (2016). Plagiarism byuniversity students: the problem and someproposals, by Brian Martin. Retrieved 7 February 2016, from https://www.uow.edu.au/~bmartin/pubs/92tert.html