Statistics Paper Review

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· Ethical Behavior of Business Students at Rocky University (350 Points)

During the global recession of 2008 and 2009, there were many accusations of unethical behavior by Wall Street executives, financial managers, and other corporate officers. At that time, an article appeared that suggested that part of the reason for such unethical business behavior may stem from the fact that cheating has become more prevalent among business students. The article reported that 86% of business students admitted to cheating at some time during their academic career as compared to 77% of non-business students.

Cheating has been a concern of the dean of the College of Business at Rocky University for several years. Some faculty members in the college believe that cheating is more widespread at Rocky than at other universities, while other faculty members think that cheating is not a major problem in the college. To resolve some of these issues, the dean commissioned a study to assess the current ethical behavior of business students at Rocky. As part of this study, an anonymous exit survey was administered to a sample of 90 business students from this year’s graduating class. Responses to the following questions were used to obtain data regarding three types of cheating.

During your time at Rocky, did you ever present work copied off the Internet as your own?

Yes

During your time at Rocky, did you ever copy answers off another student’s exam?

Yes

During your time at Rocky, did you ever collaborate with other students on projects that were supposed to be completed individually?

Yes

Any student who answered yes to one or more of these questions was considered to have been involved in some type of cheating. The complete data set is in the file named Rocky .

Managerial Report

Prepare a report (see below) for the dean of the college that summarizes your assessment of the nature of cheating by business students at Rocky University. Be sure to include the following seven (7) items in your report.

1. To summarize the data, compute the proportion of all students the proportion of all male students, and the proportion of all female students that presented

a. Work copied off the internet as their own b. Copied answers off another student’s exam c. Collaborated with other students on projects that were supposed to be completed individually.

Then comment on your findings.

1. Develop 95% confidence intervals for the proportion of all students, the proportion of all male students, and the proportion of all female students who were involved in some type of cheating.

1. Develop 95% confidence intervals for the proportion of all students, the proportion of all male students, and the proportion of all female students who were involved in copying off the internet.

1. Develop 95% confidence intervals for the proportion of all students, the proportion of all male students, and the proportion of all female students who were involved in copying off another's exam.

1. Develop 95% confidence intervals for the proportion of all students, the proportion of all male students, and the proportion of all female students who were involved in collaborating on individual project.

1. Conduct a hypothesis test to determine if the proportion of all business students at Rocky University who were not involved in some type of cheating is less than that of all business students elsewhere. Use α = 0.05.

1. What advice would you give to the dean based upon your analysis of the data?

Write a report that adheres to the Written Assignment Requirements under the heading “Expectations for CSU-Global Written Assignments” found in the CSU-Global Guide to Writing and APA Requirements . Items that should be included, but are not limited to are a title page, an introduction, a body which answers the questions posed in the problem and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments you should have in-text citations and a reference page too. Please include any tables of calculations, calculated values and graphs associated with this problem in the body.

NOTE: Submitting your Excel file will aid in grading with partial credit if errors are found in the paper.

Be sure that your report contains the following:

· A title page

· An introduction

· A body of the paper that answers the questions posed in the problem and calculations and graphs associated with this problem.

· A conclusion paragraph that addresses your findings and what you have determined from the data and your analysis.

Be sure to submit your Excel file as well.

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Statistics Paper for Review

MODULE 8: Rocky University Managerial Report

Introduction

Between 2008 and 2009, it was discovered that many in the business world (Wall Street executives, financial managers and other corporate officers) were behaving in an unethical way. It was believed that the cause of this behaviour was in part due to cheating while attending university classes. Cheating had been a concern of the Dean of the College of Business at Rocky University for many years and there was a concern that the cheating at Rocky University might be worse than at other universities.

To understand some of the issues associated with the report, the dean commissioned a study to ascertain the ethical behaviour of current business students at Rocky University. An anonymous exit survey was administered to a sample of 90 graduating students.

All statistical information can be found in the accompanying excel workbook. The students were asked three questions, namely: * Did you ever copy work off the Internet as your own? * Did you ever copy answers off another student’s exam? * Did you ever collaborate with other students on a project that was supposed to be completed individually? A total of 90 students responded to the questionnaire with the group divided into 49 male and 41 female students. Our analysis of the survey results is below:

(1) The chart below summarizes the data and computes the proportion of all students, male and female who presented work copied off the Internet as their own, copied answers off another student's exam, or collaborated with other students on projects that were supposed to be completed individually. Then comment on your findings.

MODULE 8: Rocky University Managerial Report

	Copied from Internet	Copied on Exam	Collaborated on Individual Project
Gender	Yes	No	Yes	No	Yes	No
Male	18	31	26	23	27	22
Female	16	25	20	21	22	19
Total	34	56	46	44	49	41
Proportion of all students	37.78%	62.22%	51.11%	48.89%	54.44%	45.56%
Proportion of Male	36.73%	63.27%	53.06%	46.94%	55.10%	44.90%
Proportion of Female	39.02%	60.98%	48.78%	51.22%	53.66%	46.34%

37.78% of all students presented work copied off the Internet as their own.

36.73% of male students presented work copied off the Internet as their own.

39.02% of female students presented work copied off the Internet as their own.

51.11% of all students copied answers off another student's exam.

53.06% of male students copied answers off another student's exam.

48.78% of female students copied answers off another student's exam.

54.44% of all students collaborated with other students on projects that were supposed to be completed individually.

55.10% of male students collaborated with other students on projects that were supposed to be completed individually.

53.66% of female students collaborated with other students on projects that were supposed to be completed individually.

(2) We have developed a 95% confidence intervals for the proportion of all students--the proportion of male students and the proportion of female students--who were involved in some type of cheating.

There are 90 business students in the sample in which 5 students are not involved in any type of cheating. That is, the remaining 85 students are involved in some type of cheating.

MODULE 8: Rocky University Managerial Report

95% confidence interval for the proportion of all students who were involved in some type of cheating is given by

where p = x/n = 85/90 = 0.944444444, = 1.959963985, n = 90

= (0.8971, 0.9918)

Thus with 95% confidence we can claim that the proportion of all students who were involved in some type of cheating is within (89.71%, 99.18%).

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	90
Number of Successes	85
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.944444444
Z Value	-1.959963985
Standard Error of the Proportion	0.024145194
Interval Half Width	0.047323711

Confidence Interval
Interval Lower Limit	0.8971
Interval Upper Limit	0.9918

In the sample there are 49 males in which 7 are not involved in any type of cheating. That is, the remaining 42 males are involved in some type of cheating.

95% confidence interval for the proportion of male students who were involved in some type of cheating is given by

where p = x/n = 42/49 = 0.857142857, = 1.959963985, n = 49

= (0.7592, 0.9551)

MODULE 8: Rocky University Managerial Report

Thus with 95% confidence we can claim that the proportion of males who were involved in some type of cheating is within (75.92%, 95.51%).

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	49
Number of Successes	42
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.857142857
Z Value	-1.959963985
Standard Error of the Proportion	0.049989587
Interval Half Width	0.097977789

Confidence Interval
Interval Lower Limit	0.7592
Interval Upper Limit	0.9551

In the sample there are 41 females in which 6 are not involved in any type of cheating. That is, the remaining 35 females involved in some type of cheating.

95% confidence interval for the proportion of female students who were involved in some type of cheating is given by

where p = x/n = 41/35 = 0.853658537, = 1.959963985, n = 41

= (0.7, 1)

Thus with 95% confidence we can claim that the proportion of females who were involved in some type of cheating is within (70%, 100%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	41
Number of Successes	35
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.853658537
Z Value	-1.959963985
Standard Error of the Proportion	0.055199337
Interval Half Width	0.108188713

Confidence Interval
Interval Lower Limit	0.7
Interval Upper Limit	1.0

(3) A 95% confidence intervals for the proportion of all students--the proportion of male students and the proportion of female students--who were involved in copying off the Internet was developed.

95% confidence intervals for the proportion of all students who were involved in copying off the Internet is given by,

where p = x/n = 49/90 = 0.544444444, = 1.959963985, n = 90

= (0.4416, 0.6473)

Thus with 95% confidence we can claim that the proportion of all students who were involved in copying off the Internet is within (44.16%, 64.73%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	90
Number of Successes	49
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.544444444
Z Value	-1.959963985
Standard Error of the Proportion	0.052495999
Interval Half Width	0.102890267

Confidence Interval
Interval Lower Limit	0.4416
Interval Upper Limit	0.6473

95% confidence interval for the proportion of male students who were involved in copying off the Internet is given by

where p = x/n = 18/49 = 0.367346939, = 1.959963985, n = 49

= (0.2324, 0.5023)

Thus with 95% confidence we can claim that the proportion of males who were involved in copying off the Internet is within (23.24%, 50.23%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	49
Number of Successes	18
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.367346939
Z Value	-1.959963985
Standard Error of the Proportion	0.068868874
Interval Half Width	0.134980512

Confidence Interval
Interval Lower Limit	0.2324
Interval Upper Limit	0.5023

95% confidence interval for the proportion of female students who were involved in copying off the Internet is given by

where p = x/n = 16/41 = 0.390243902, = 1.959963985, n = 41

= (0.2409, 0.5396)

Thus with 95% confidence we can claim that the proportion of females who were involved in copying off the Internet is within (24.09%, 53.96%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	41
Number of Successes	16
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.390243902
Z Value	-1.959963985
Standard Error of the Proportion	0.076182323
Interval Half Width	0.149314609

Confidence Interval
Interval Lower Limit	0.2409
Interval Upper Limit	0.5396

(4) Develop 95% confidence intervals for the proportion of all students--the proportion of male students and the proportion of female students--who were involved in copying off another's exam.

95% confidence intervals for the proportion of all students who were involved in copying off another's exam is given by,

where p = x/n = 45/90 = 0.50, = 1.959963985, n = 90

= (0.3967, 0.6033)

Thus with 95% confidence we can claim that the proportion of all students who were involved in copying off another's exam is within (39.67%, 60.33%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	90
Number of Successes	45
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.5
Z Value	-1.959963985
Standard Error of the Proportion	0.052704628
Interval Half Width	0.103299172

Confidence Interval
Interval Lower Limit	0.3967
Interval Upper Limit	0.6033

95% confidence interval for the proportion of male students who were involved in copying off another's exam is given by

where p = x/n = 26/49 = 0.530612245, = 1.959963985, n = 49

= (0.3909, 0.6703)

Thus with 95% confidence we can claim that the proportion of males who were involved in copying off another's exam is within (39.09%, 67.03%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	49
Number of Successes	26
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.530612245
Z Value	-1.959963985
Standard Error of the Proportion	0.071294573
Interval Half Width	0.139734795

Confidence Interval
Interval Lower Limit	0.3909
Interval Upper Limit	0.6703

95% confidence interval for the proportion of female students who were involved in copying off another's exam is given by

where p = x/n = 20/41 = 0.5487804878, = 1.959963985, n = 41

= (0.3348, 0.6408)

Thus with 95% confidence we can claim that the proportion of females who were involved in copying off another's exam is within (33.48%, 64.08%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	41
Number of Successes	20
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.487804878
Z Value	-1.959963985
Standard Error of the Proportion	0.078063651
Interval Half Width	0.153001945

Confidence Interval
Interval Lower Limit	0.3348
Interval Upper Limit	0.6408

(5) Develop 95% confidence intervals for the proportion of all students--the proportion of male students and the proportion of female students--who were involved in collaborating on what was meant to be an individual project.

95% confidence intervals for the proportion of all students who were involved in collaborating on what was meant to be an individual project is given by,

where p = x/n = 45/90 = 0.50, = 1.959963985, n = 90

= (0.3967, 0.6033)

Thus with 95% confidence we can claim that the proportion of all students who were involved in collaborating on what was meant to be an individual project is within (39.67%, 60.33%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	90
Number of Successes	45
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.5
Z Value	-1.959963985
Standard Error of the Proportion	0.052704628
Interval Half Width	0.103299172

Confidence Interval
Interval Lower Limit	0.3967
Interval Upper Limit	0.6033

95% confidence interval for the proportion of male students who were involved in collaborating on what was meant to be an individual project is given by

where p = x/n = 27/49 = 0.551020408, = 1.959963985, n = 49

= (0.4118, 0.6903)

Thus with 95% confidence we can claim that the proportion of males who were involved in collaborating on what was meant to be an individual project is within (39.67%, 60.33%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	49
Number of Successes	27
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.551020408
Z Value	-1.959963985
Standard Error of the Proportion	0.071055729
Interval Half Width	0.139266671

Confidence Interval
Interval Lower Limit	0.4118
Interval Upper Limit	0.6903

95% confidence interval for the proportion of female students who were involved in collaborating on what was meant to be an individual project is given by

where p = x/n = 22/41 = 0.536585366, = 1.959963985, n = 41

= (0.3839, 0.6892)

Thus with 95% confidence we can claim that the proportion of females who were involved in collaborating on what was meant to be an individual project is within (38.39%, 68.92%).

MODULE 8: Rocky University Managerial Report

Details

Confidence Interval Estimate for the Proportion

Data
Sample Size	41
Number of Successes	22
Confidence Level	95%

Intermediate Calculations
Sample Proportion	0.536585366
Z Value	-1.959963985
Standard Error of the Proportion	0.077877564
Interval Half Width	0.152637220

Confidence Interval
Interval Lower Limit	0.3839
Interval Upper Limit	0.6892

(6) Conduct a hypothesis test to determine if the proportion of business students at Rocky University who were not involved in some type of cheating is less than that of business students elsewhere. Use α = 0.05.

The null hypothesis tested is

H0: The proportion of business students at Rocky University who were not involved in some type of cheating ≥ 0.14. (p ≥ 0.14)

The alternative hypothesis is

H1: The proportion of business students at Rocky University who were not involved in some type of cheating < 0.14. (p < 0.14)

The test statistic used is, where p = 5/90 = 0.055555556, n = 90, p0 = 0.14

Therefore, = -2.308761619

MODULE 8: Rocky University Managerial Report

Rejection criteria: Reject the null hypothesis, if the calculated value of Z is less than the critical value of Z at the 0.05 significance level.

Lower critical value = -1.644853627

Conclusion: Reject the null hypothesis, since the calculated value of Z is less than the critical value of Z. The sample provides enough evidence to conclude that the proportion of business students at Rocky University who were not involved in some type of cheating is less than that of business students elsewhere.

Details

Z Test of Hypothesis for the Proportion

Data
Null Hypothesis  =	0.1400
Level of Significance	0.05
Number of Items of Interest	5
Sample Size	90

Intermediate Calculations
Sample Proportion	0.055555556
Standard Error	0.036575645
Z Test Statistic	-2.308761619

Lower-Tail Test
Lower Critical Value	-1.644853627
p-Value	0.010478406
Reject the null hypothesis

(7) What advice would you give to the dean based upon your analysis of the data?

Although the percentage of students who did cheat during their academic career is more than other institutions, it is a serious problem and needs to be addressed by the Dean of Students. Some possible recommendations are outlined below:

1. Require that each student review and sign a Code of Ethics each school year.

2. Create online ethical compliance training for all incoming students.

3. Conduct this survey to both incoming freshman and use the same students when they exit the school to see any differences and see if the programs are working.

4. Incorporate “Accountability” courses so that they understand what this really means.

5. Understand that the students will learn when they are ready to learn and not when we are ready to teach them. This means that they must teach this at every corner and behave ethically at all times, so when they are ready they learn the right way to do it. Conclusion:

62.22% of the business students were not involved in copying off the Internet. 48.89% of the business students were not involved in copying off another's exam and 45.56% of the business students were not involved in collaborating on what was meant to be an individual project. The proportion of business students at Rocky University who were not involved in some type of cheating is less than that of business students elsewhere.

The business students at Rocky University need to be re-educated on the merits of doing their own work and not utilizing their classmates’ work in order to pass their courses. Using the above described steps to institute some methods to reduce the number of cheating students would be a good road for Rocky University to take. Comparing today’s numbers and calculations to those of the business students after a four-year period would be instrumental in understanding whether or not the steps are helping in any way.

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