Managerial Report Using Statistics Term Papers Example

Introduction

In this paper we apply the basic techniques of statistics and probability theory related to a real world problem. The research is related to substance abuse as a problem at universities and colleges of the United States. Many companies are really worrying about the impact of substance abuse on their future employees. It was reported that 46% of the United States students have been involved in some type of substance abuse. In this case we consider Rocky University. We would like to investigate is substance abuse is a real problem in this university or it is not a major problem.

Body

We are given with a data set of 90 students. They responded for three questions regarding the type of substance abuse they have been involved (They answered simply – Yes or Not). Also gender of each student was recorded. There are following variables are considered:

Involved in Binge Drinking – whether the student was involved in binge drinking

Abused Prescription Med. or Marijuana – whether the student was abused prescription medication or marijuana
Used Illegal Drugs – whether the student used illegal drugs
Gender – gender of the student
We summarize the answers on three questions calculating the number of “Yes” and “No”:
During your time at Rocky, did you ever participate in binge drinking? Yes: 22, No: 68.
During your time at Rocky, did you ever abuse prescription medication? Yes: 25, No: 65.
During your time at Rocky, did you ever use any type of illegal or illicit drug (not included in questions 1 or 2)? Yes: 25, No: 65.
The purpose of this research paper is to prepare a report for the president of the university that summarizes our assessment of the nature of substance abuse by students at Rocky University. We start with summarizing the data, computing proportion of all male students and all female students who was involved on each type of substance abuse.

Males:

For binge drinking:
p=1346≈0.283

For prescription medication:

p=1246≈0.261

For illegal or illicit drugs:

p=1046≈0.217

Females:

For binge drinking:
p=944≈0.205

For prescription medication:

p=1344≈0.295

For illegal or illicit drugs:

p=1544≈0.341
We can see that males are more involved in binge drinking than females (28.3% and 20.5%). But instead females are more involved in other two types of substance abuse: prescription medication (males – 26.1%, females – 29.5%) and illegal drugs (males – 21.7%, females – 34.1%).
The next step is to develop 90% confidence interval for the proportion of all students and for males and females separately who were involved in some type of substance abuse.

Test and CI for One Proportion: Involved in ; Abused Presc; Used Illegal

Event = 1

Variable X N Sample p 90% CI

Involved in Binge Drinki 22 90 0,244444 (0,171663; 0,330309)
Abused Prescription Med. 25 90 0,277778 (0,201051; 0,365843)
Used Illegal Drugs 25 90 0,277778 (0,201051; 0,365843)
We are 90% confident that the population proportion of each of three types of substance abuse for all students is between the limits mentioned in column 90% CI (see above).

For males separately:

Test and CI for One Proportion: Involved in ; Abused Presc; Used Illegal
Event = 1

Variable X N Sample p 90% CI

Involved in Binge Drinki 13 46 0,282609 (0,175979; 0,411320)
Abused Prescription Med. 12 46 0,260870 (0,157962; 0,388130)
Used Illegal Drugs 10 46 0,217391 (0,122961; 0,340794)
We are 90% confident that the population proportion of each of three types of substance abuse for male students is between the limits mentioned in column 90% CI (see above).

For females separately:

Test and CI for One Proportion: Involved in ; Abused Presc; Used Illegal
Event = 1

Variable X N Sample p 90% CI

Involved in Binge Drinki 9 44 0,204545 (0,111075; 0,329800)
Abused Prescription Med. 13 44 0,295455 (0,184455; 0,428170)
Used Illegal Drugs 15 44 0,340909 (0,223257; 0,475387)
We are 90% confident that the population proportion of each of three types of substance abuse for female students is between the limits mentioned in column 90% CI (see above).
The goal of analysis is to answer the main question: is the proportion of all students at Rocky University who were not involved in some type of substance abuse isles that that of all United States elsewhere. To do this we use t-test for proportion. We know that on average, 46% of the U.S. students have been involved in some type of substance abuse. Hence, 54% were not involved. Now we must calculate the proportion of the students in the sample, who have answered “No” for all three questions:
p=4390≈0.478
The null hypothesis is: The proportion of the students in Rocky University who were not involved in any type of substance abuse does not significantly differ from the average proportion across the U.S.
The alternative hypothesis: The proportion of the students in Rocky University who were not involved in any type of substance abuse is significantly less than the average proportion across the U.S.
H0:p=0.54Ha:p<0.54a=0.10

Test and CI for One Proportion

Test of p = 0,54 vs p < 0,54

90% Upper Exact

Sample X N Sample p Bound P-Value
1 43 90 0,477778 0,550610 0,140
Since p-value of the test is 0.14 and it is lower than level of significance alpha, we can’t reject the null hypothesis. There is no enough evidence to support the claim that the proportion of the students in Rocky University who were not involved in any type of substance abuse is significantly less than the average proportion across the U.S (at 10% level of significance).

Conclusion

According to the results of our research, we can say the president of the university that the level of substance abuse in his university is not lesser than on average across the United States. That’s why this problem cannot be considered as insignificant problem. We strongly recommend to the students and faculty to pay attention to this problem and reduce the level of substance abuse as soon as possible. Business community should inform students about potential problems in finding a job for those who are regularly involved in substance abuse. Students must understand the responsibility of living in such lifestyle.

References

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochran, J.J. (2015). Essentials of statistics for business and economics. (7th ed.). Stamford, CT: Cengage Learning.
Gut, Allan (2013). Probability: A Graduate Course (2 ed.). New York, NY: Springer. ISBN 978-1-4614-4707-8.
Gillies, Donald (2000); "Philosophical Theories of Probability"; Routledge; Chapter 4 "The subjective theory"