Statistics Project Survey - Report Example

Statistic Project Statistic Project Background of the problem The global recession that was witnessed in 2008 to 2009 in US had adverse implications for the management operations. For instance, there were increased allegations of unethical business behaviour among the management officials and the executives; an observation that was made by the Wall Street Executives, Corporate Officers and the Financial Managers. Consequently, an article posted claimed that such unethical business affairs and behaviours could have stemmed from the massive cheating among the college students, especially the business students, within their academic career period. Additionally, the article postulated that 86% of the business students admitted to be involved in cheating as opposed to 77% of the non-business counterparts at some time during their academic journey. In response to this, the Dean of Rocky Business College wants to ascertain the rumours that his college had prevailed in cheating than any other University. Therefore, the Dean commissioned a survey study to assess the cheating prevalence in Rocky University. The study made use an anonymous exit survey that was administered to a sample of 90 students (n=90) for the acquisition of reliable results and reduce non-respondent rates. The data collected was captured in an excel sheet and subjected to the statistical analysis that aimed to assess the prevalence of cheating among the students, as well as, for the genders. Three independent variables were established with cheating being the only dependent variable. Gender was determined by providing more insights regarding unethical behaviour between the two genders. A 95% confidence level was used in the data analysis. The variables included; Students who copied from the Internet (CI) Students who copied from other student’s work during Exams (CE) Collaboration on individual projects (CIP) Report findings Summary of the data Proportion of gender used in the sample Pie chart 1: Showing proportion of gender of the sample Proportions of Yes and No responses for all the three variables Bar chart: Showing Yes and no proportions for CI, CE and CIP Proportion of students who copied from the Internet (CI) and associated gender A column chart: showing the proportion of gender that copied from the Internet Proportion of the students who copied exams A column chart: showing the proportion of gender that copied exams Proportion of students who collaborated on individual project Cylindrical chart: CIP gender proportions Table of summary   Copied from Internet Copied on Exam Collaborated on Individual Project Gender Yes No Yes No Yes No Male 24 20 24 20 19 25 Female 18 28 24 22 26 20 Total 42 48 48 42 45 45 Proportion of all students 46.67% 53.3% 53.3% 46.67% 50% 50% Proportion of Male 57.1% 41.67% 50% 47.6% 42.2% 55.56% Proportion of Female 42.8% 48.3% 50% 52.4% 57.8% 44.44% Comment on the findings From the above data summary it is revealed that both the female and male students were involved in some type of cheating whether from the Internet, copying from friends during exams or even collaborating on individual projects. Accordingly, most of the students copied exams from other students as opposed to the Internet and collaboration of the individual projects as indicated by a 53.3% of the CE proportions. Collaborations in individual projects reveal a 50/50 proportion indicating that half of the projects submitted in Rocky are not genuine. Such students do not follow academic research ethics and such aspects have a high probability of being translated to the work place environment (Bernstein, 2009). Additionally, the male students have revealed a high prevalence of cheating via copying from the internet as opposed to the female (57.1% vs. 42.8%). This indicates that males have a higher probability of showing unethical behaviour related to the Internet as they seem to rely much on it. Collaboration on individual projects has been depicted to show equal results in its proportions (50% vs. 50%). This indicates that all the evaluations tests presented to these students do not reflect their capabilities and autonomy, effectively. The individual projects presented at the end of the course are essential tools to evaluate students on research techniques and ethics in research. Collaboration has been prevalent among the females as opposed to the males (57.8% vs. 42.2%). Moreover, the figures depicted under each variable are scary and may suggest that future students may not be relied in any corporate environment. It may concluded that, 46.7% of all Rocky students rely on the Internet to do their assignments, 53.3% of the total population rely on copying from friends during exams and 50% of the total students present unoriginal projects. Hence it can be concluded that, at least 46.7% of Rocky’s university population is involved in some kind of cheating (Bernstein, 2009). Therefore, the Dean has not been taking the corrective measures mitigate this problem; hence there will be continued challenge of unethical practices in the corporate environment, ceteris paribus. Part two Confidence Interval for all students involved in cheating Given n = 90, 8 of the students never cheated, therefore, the remaining 82 students cheated hence a 95% CI that the students were involved in cheating can be constructed as follows; Where p = x/n = 82/90 = 0.91111, Zα/2 = 1.96, n= 90 Therefore, CI = (0.852, 0.970) Thus with 95% CL, it can be claimed that the proportion of the business students in Rocky who are involved in cheating is within 85.2% and 97% (Smithson, 2003) (As shown in Output 1). In the given sample, there are 44 males in which 4 of them do not cheat in any of the three types indicating that 40 of them have cheated. Constructing a 95% CI of the males who are involved in cheating is given by; Where P = x/n = 40/44 = 0.9090, Zα/2 = 1.96 However, n = 44 Therefore, the interval limits is given as = (0.824, 0.994) Therefore, it can be concluded that with a 95% CL we can claim that the proportion of the males who have cheated in Rocky University is within 82.4% and 99.4% (As shown in Output 2) On the other hand, there are 46 females in the sample of which 4 of them do not cheat in any type of cheating indicating that 42 of them have ever cheated (Smithson, 2003). Where P = x/n = 42/46 = 0.9130, Z= 1.96 (under 95%CL) Therefore, from Excel output 3, the limits can be calculated as; Confidence Interval limits = 0.832, 0.994 It can be concluded that the proportion of females who cheat lies within 83.2% and 99.4% with a 95% CL. Part three Confidence Intervals for the proportion of the students who copied from the Internet using a 95% CL can be given as; X= 42 (students who copied from Internet) and n = 90 and p = x/n = 42/90 = 0.46667, Z = 1.96 (at 95% CL) Confidence limits are given as= 0.316, 0.618 (under 95% CL) (Output 4) It can be concluded that, using 95% Confidence level, the students who copied from the Internet lies within 31.6% and 61.8%. The Confidence Interval for the male students who copied from the Internet can be illustrated as; X = 24 and n= 42 (Males who copied from Internet P can be calculated as x/n = 24/42 = 0.5714, under 95% Z = 1.96 (Smithson, 2003) Therefore, the limits can be given as = 0.422, 0.721 (Output 5) It can be concluded that the population of the male students who copy from the internet lies within 42.2% and 72.1% of the total population using 95% CL. Similarly, the confidence Interval for the female proportion can be calculated in the same way; Female who copy from Internet = x = 18 and n = 42 Where p = x/n = 18 / 42 = 0.4285, Z = 1.96 Therefore, the limits are given as = 0.279, 0.578 (Output 6) It can be said that the female proportion that cheats lie within 27.9% and 57.8% of the total population using a 95% Confidence Level. Part four Confidence interval of the students who copied off another’s work during exams can be calculated as; For the proportion that copied off exams, using 95% CL the Confidence Interval can be given as; X = 48 and n = 90 where p = x/n = 48/90 = 0.53333, Z = 1.96 (95% CL) The limits can be given as = 0.392, 0.674 It can be concluded that the proportion of the students who copy exams in Rocky University lie within 39.2% and 67.4% using 95% CL. For the proportion of the males who copied off from other’s work the Confidence Interval can be given as; X = 24 n = 48 Where p = x/n = 24 / 48 = 0.5, Z = 1.96 The limits are given as = 0.359, 0.641 (Output 8) It can be concluded that the proportion of the students who copy off other’s work during exams lie within 35.9% and 64.1% with a 95% Confidence level. For the male proportion, X = female the results limits will be the same as that of the males since they have same proportions (50% vs. 50%) Part five Confidence Interval for the students who collaborated on individual’s project can be constructed as follows; Students who collaborated for individual project = X = 45, n = 90 Where p = x/n = 45 / 90 = 0.5, Z = 1.96 (95% CL) The limits are given as = 0.359, 0.641 (Output 9) Students who collaborated on individual projects have their proportion lie within a confidence Interval of 35.9% and 64.1% of the total population given a 95% Confidence Level. For the male proportion the confidence interval may be constructed as; X = 16, n = 45 Where p = x/n = 16 / 45 = 0.35556, Z = 1.96 (95% CL) The limits are given as = 0.216, 0.495 (Output 10) From the above limits it can be concluded that the proportion of the male students who collaborate for individual project lie within 21.6% and 49.5% of the population with 95% confidence level. For the females, the confidence interval takes the parameters X = 29, n = 45 Where p = x/n = 29 / 45 = 0.64444, Z = 1.96 (95% CL) The limits are given as = 0.505, 0.784 (Output 11) It can be concluded that the proportion of the female students who collaborated in individual projects lie within 50.5% and 78.4% of the total population. Part 6 Hypothesis Testing The hypothesis aims at determining if the proportion of Rocky’s business students involved in cheating is less than that of the other business students in other parts using SL = 0.05 Statement of hypothesis H1: Rocky’s proportion of students who never indulged in some type of cheating ≥ 0.14 (p ≥ 0.14) H0: Rocky’s proportion that never indulged in some type of cheating < 0.14 (p < 0.14) 0.14 is reflected in output 12 (the lower limit) Z is the best test statistic that can be given as P = X/n = 8/90 = 0.088889, n = 90 Po = 0.14 Substitute p, Po and n. Therefore, Z = 0.08889 – 0.14 = -0.0511 / 0.03657 = - 1.3973 √0.14 (1-0.14) / 90 Rule of thumb: Reject H0, if the Z calculated is less the Z critical value at 0.05 (Van, 2002) Since we are interested with the proportion of students being less than elsewhere, we consider one-tailed distribution (the lower critical value) = -1.644 (Consider absolute values of the Z score) Therefore, Z calculated is less than the Z critical hence Reject H0 and concluded that the business students at Rocky business college who do not indulge in some type of cheating is less than that of other business students elsewhere as seen from the study. However, there is still a room to examine the phenomenon at significance levels of 0.01 and 0.1 to compare the results. Part 7 Conclusion and recommendation From the study, it can be concluded that 54.33% of the students never copied from the Internet, 47.7% never copied other’s work during exams while 50% of the students never collaborated in individual’s projects. The proportion of the students that indulged in some type of cheating was less than of other business students elsewhere (Bernstein, 2009). Therefore, the Dean has to address the cheating among his students through a number of suggested alternatives. First, the Dean may implement the signing and reviewing a Code of Ethics annually for the students. Severe disciplinary actions must be initiated which may even lead to termination or discontinuity for the cheating students. Additionally, surveys for the freshman and as they exit school should be initiated to evaluate the effectiveness of the implemented programs. Lastly, the Dean has to incorporate accountability courses within the school programs to ensure students understand the benefits of self-evaluation, autonomy and independence of doing exams on their own. These are the binding aspects of ethics hence they will understand the need of doing personal work that is original as opposed to copying off from external sources (cheating). References Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochrane, J.J. (2015). Essentials of statistics for business and economics (7th ed.). Mason, OH: South- Western Cengage Learning Bernstein, S., & Bernstein, R. (20099). Inferential statistics. (Schaums outline of theory and problems of elements of statistics.) New York: McGraw-Hill. Van, B. G. (2002). Statistical rules of thumb. New York: Wiley-Interscience. Smithson, M. (2003). Confidence intervals. Thousand Oaks, Calif: Sage Publications. Read More