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The Statistical Analysis of

Students Using

Personal Coffee Mugs

At the

University of Vermont

Stat 211

Spring 2006

George Fowler

ABSTRACT

A research project was conducted at the University of Vermont to determine if a student is more likely to use a personal coffee mug if they study at a particular college on campus. The research showed a student is more likely to use a personal coffee if they studied at the Math & Engineering or Rubenstein schools.

INTRODUCTION

The University of Vermont is a beacon of education and awareness for many students and community members who live in a state with a long standing tradition of environmental conservation. As one of the state’s larger employers and whose research helps to shape many state policies concerning the environment, UVM is a symbol of Vermont’s heritage in the national and international spotlight.

Students studying at UVM are the next generation of future representatives of Vermont’s proud tradition. UVM shapes their students’ academic endeavors by hiring respected lecturers and researchers. Students also mold their own future by inundating themselves in the local and academic communities. Their behaviors on and off campus reflect their professional and education development at UVM. An observation of these behaviors can provide an outsider with a snapshot of their development as future ambassadors of Vermont.

The behavior of interest in this study is how University of Vermont’s students drink their coffee or other hot beverages. The majority of coffee cups sold at UVM find their way into waste baskets and land fills only after one use. This behavior at first might appear to be insignificant, however upon further investigation, the amount of waste generated by disposable coffee cups over the course of a week, a semester or a four year degree, is implausible.

This research attempts to identity if a student is more likely to use a personal coffee mug if he or she belongs to a particular college at UVM. The research will answer this question by proving a statistical significance exists between the college of study (for example, Arts & Sciences) in a sample of students who use reusable coffee containers. This proportion will be compared to the true proportion of what college UVM students belong to. The population of interest is the students of UVM who use reusable coffee containers.

The answers could provide clues to the positive deviant behavior of students who choose use personal coffee containers. Future research could lead to a program to raise awareness among the entire student body in hopes of reducing the amount of waste produced on campus and strengthen Vermont’s future representatives.

METHODS

The researcher gathered data at multiple sites at the University of Vermont. The General Manager of dining services at UVM was contacted to discuss potential sites of interests. The researchers choose an interviewing method and conducted stratified random sampling to collect data.

The researcher split the population of interest into groups based on the sites of where they purchased their coffee. The time and location of each site to conduct interviews on a specified day was chosen at random. Before the final sites were chosen, each site’s geographic location was assessed to avoid choosing a site whose proximity was close to a building with a high concentration of one college’s classes. For example, a coffee selling site near the medical college, or the math and engineering building would not have been selected as a final site. Also, the times and site locations were chosen at random to reduce the influence of class starting times.

Population: College Name Proportion Proportion Sample: College Name Arts & Sciences 0.48 0.39 Arts and Sciences Rubenstein 0.06 0.23 Rubenstein Math and Engineering 0.07 0.18 Math and Engineering Education 0.13 0.14 Education Agriculture 0.10 0.05 Agriculture Business 0.09 0.02 Business Other 0.07 0.00 Other

For Raw Data, please refer to Addendum 1.

According to UVM’s Source Book for the Fiscal Year 2006, there are a total of ten different colleges students could be studying in. Non-degree students, staff and faculty were not included in the final statistical analysis. At three of these colleges, could only include graduate students so these programs were lumped with the Nursing college to form the “other” category.

From our sampling, the research was able to gather information from forty four respondents. The respective proportion of schools the respondents belonged to is noted in table 2.1 and 2.

Graphical

I Pie Chart

Table 2.1 Table 2.

Pie Chart of Population: College Proportion (^) Arts and Sciences Rubenstein Math and Engineering Education Agriculture Business Other

Pie Chart of Sample: College Proportion (^) Arts & Sciences

Rubenstein Math and Engineering Education Agriculture Business Other

Table 2.1 and 2.2 display the proportion of the Population and the Sample in a chart form.

II Bar Chart II Normality Chart of Sample

Table 2.3 Table 2.

Value

Category BusinessOther EducationAgriculture

Math Arts&SciencesRubenstein

20

15

10

5

0

ExpectedObserv ed

Chart of Observed and Expected Values

C

Percent

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.

99 95 90 80 70 (^6050) (^4030) 20 10 5 1

MeanStDev 0.14430. NAD (^) 0.270 7 P-Value 0.

Probability Plot of Sample Data Normal

Table 2.3 displays the expected proportions or target values in the survey. The researcher derived this value from the proportion rate of the total student population at UVM and what college they currently study in. The observed proportion is the actual results uncovered in the research.

The researcher conducted a normalcy test on the distribution of the sample’s probability. The purpose of this graph was to determine if the data was normally distributed which is an indication that a robust sample was collected. The P-value of this graph is 0.511. The sample has a normal distribution.

II Inferential Analysis

A. Comparison Based on College of Study

Before an analysis could be conducted a null hypothesis (Ho) and alternative hypothesis (Ha) was generated to prove if a statistical significance was present.

Ho: O 1 =E 1

The proportion of the observed outcome is equal to the proportion of the observed outcomes.

Ha: O 1 ≠E 1

N DF Chi-Sq P-Value 44 3 33.0620 0.

After running the analysis a second time, using the same hypothesis and confidence interval, the observed values remain statistically different from than the expected values. The corresponding graphs, 3.2 and 3.3 are listed below.

Table 3.2 Table 3.

Category

Contributed Value

Rubenstein Math Other Arts

20

15

10

5

0

Chart of Contribution to the Chi-Square Value by Category

Value

Category Arts Rubenstein Math Other

20

15

10

5

0

ExpectedObserved

Chart of Observed and Expected Values

The analysis begins to loose its meaningful significance when groups are combined with each other. The inferential value of the analysis decreases when groups are combined because we can not compare individual groups with each other because they are lumped together.

The analysis was run a third time to demonstrate a statistical significance exists when all groups have at least five respondents in the observed and expected groups. However, even though there still is statistical significance between the observed and the expected groups, the analysis offers little inferential significance since many of the colleges have been lumped together.

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: C9C

Test Contribution Category Observed Proportion Expected to Chi-Sq 1 17 0.48 21.12 0.8037 Arts & Sciences 2 18 0.13 5.72 26.3634 Education, Math & Engineering 3 9 0.39 17.16 3.8803 Other, Agriculture, Business N DF Chi-Sq P-Value 44 2 31.0473 0.

D. Comparison Based on Sex

The researcher also collected information about the sex of each respondent. This was obtained by the researcher’s observation. The researcher also wanted to analysis if a person was more likely to use a personal coffee container depending on their sex. The researcher choose two methods to analyze the data. The first, a Chi-square test was used to test if the observed data differed from the expected. The hypothesis, confidence interval and α remain the same as in the Comparison Based on College of Study.

Males and Females Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: C Test Contribution Category Observed Proportion Expected to Chi-Sq

1 24 0.56 24.64 0. 2 20 0.44 19.36 0.

N DF Chi-Sq P-Value 44 1 0.0377804 0.

These results show a P-Value of .846. This is greater than our α value so we fail to reject the null hypothesis and conclude our data is not statistically significant. The sex of a person does not make a person more likely to use a personal coffee container.

The second test, the test of One Proportion also was used to see if a statistical significance exists. The results of this test are below. The hypothesis, confidence interval and α remains the same.

Test and CI for One Proportion Test of p = 0.5 vs p not = 0. Exact Sample X N Sample p 95% CI P-Value 1 24 44 0.545455 (0.388472, 0.696093) 0.

This test displays that the data is not statistically significant.

DISCUSSION

The data shows that a students belonging to a particular college is more likely to use a personal coffee mug. Tables 2.2 and 2.3 display that students who attend the Rubenstein and the Math and Engineering colleges are more likely to use a personal coffee mug.

If no significance was present, the research should have found three Rubenstein students and three Math and Engineering students in the sample group. However, ten and eight students were found respectively. This difference contributed greatly to the Chi Square statistic, more than double of other groups’ contributions to the Chi Square. The larger the contribution to the Chi-Square the larger the difference between observed and expected values. This answers the research question posed, “is a student is more likely to use a personal coffee mug if he or she belongs to a particular college at UVM?” A student is more likely to use a personal coffee mug if they attend the Rubenstein and Math and Engineering Schools at UVM.

The second question posed in this research question is if the sex of a student has a significance on whether or not they use a personal coffee mug. A sample of forty four students was obtained and this satisfied the condition of the Central Limit Theorem. This allowed the researcher to use two data analyses to test for statistical difference. Both results of these tests showed there is no statistical difference between the sexes in whether or not one is more likely to use a personal coffee container.

While this research was being conducted, the researcher collected other background information related to this subject. The researcher wanted a snapshot image of the amount of coffee being sold on a weekly basis at the various interviewing sites. The following data was provided by the Dining Services General manager and the manager of one of the cafes.

Table 4.

Place # of Beverages

Sold

Using Personal

Coffee Container

% of Sales using Personal Container

Alice’s Café 1307 126 10%

I Population A. Head Count of Enrolment-By College (Spring 2006)

B. Total Head Count of Students-By Sex (Fall 2005)

Population: College Name

Proportion

Proportion Sample: College Name

Arts & Sciences

Arts and Sciences

Rubenstein

Rubenstein

Math and Engineering

Math and Engineering

Education

Education

Agriculture

Agriculture

Business

Business

Other

Other

Percentage

Male

Female

Total

Success Rate

Population Data was made available by the Department of Institutional Studies at the University of VermontOther Category includes Nursing, Medicine, Cell and Molecular Biology II Sample Data A. Responses to Survey-By College (Spring 2006) Arts & Sciences

Agricultural

Group

# Of Times DrinkPurchased Per week

# Of Times Container UsedPer Week

Sex F

Sex M

Reason

A^

3

1

F^

Convenience

A^

3

F^

Environmental

A^

2

F^

Environmental

A^

10

10

F^

Environmental

A^

14

14

M^

Environmental

A^

4

3

F^

Convenience

A^

F^

Convenience

A^

10

10

F^

Environmental

A^

6

6

F^

Environmental

A^

7

7

M^

Convenience

A^

9

M^

Environmental

A^

2

2

F^

Convenience

A^

5

3

M^

Economical

A^

5

5

F^

Convenience

A^

5

5

M^

Environmental

A^

7

7

F^

Convenience

A^

M^

Economical

Average

6.

5.

Total

11

6

Number ofRespondents

17

Proportion ofSample Size(Success)

0.

Group

# Of Times DrinkPurchased Per week

# Of Times Container UsedPer Week

Sex F

Sex M

Reason

F^

M^

Environmental

F^

M^

Environmental

Average

Total

Number ofRespondents

Proportion ofSample Size(Success)

Rubenstein School of Natural Resources

Education and Social Services

Group

# Of Times DrinkPurchased Per week

# Of Times Container UsedPer Week

Sex

Reason

R^

7

5

F^

Environmental

R^

4

4

F^

Environmental

R^

6

6

M^

Economical

R^

12

12

M^

Economical

R^

5

4

M^

Environmental

R^

7

7

M^

Environmental

R^

M^

Convenience

R^

7

6

M^

Convenience

R^

6

6

M^

Economical

R^

5

5

M^

Environmental

Average

6.

6.

Total

2

8

Number ofRespondents

10

Proportion ofSample Size(Success)

0.

Group

# Of Times DrinkPurchased Perweek

# Of TimesContainer UsedPer Week

Sex F Sex M

Reason

E^

5

5

F^

Convenience

E^

4

4

F^

Environmental

E^

7

F^

Economical

E^

F^

Convenience

E^

5

F^

Convenience

E^

F^

Economical

Average

6.

5.

Total

6

Number ofRespondents

6

Proportion ofSample Size(Success)

0.

Math and Engineering

Business

Group

# Of Times DrinkPurchased Per week

# Of Times Container UsedPer Week

Sex F Sex M

Reason

M^

5

3

F^

Convenience

M^

5

F^

Convenience

M^

10

10

M^

Convenience

M^

10

10

M^

Convenience

M^

7

7

F^

Economical

M^

7

7

F^

Economical

M^

M^

Environmental

M^

21

21

F^

Environmental

Average

8.

8.

Total

5

3

Number ofRespondents

8

Proportion ofSample Size(Success)

Group

# Of Times DrinkPurchased Per week

# Of Times Container UsedPer Week

Sex F

Sex M

Reason

B^

6

6

M^

Economical

Average

6

6

Total

1

Number ofRespondents

1

Proportion ofSample Size(Success)

0.

B. Responses to Survey- By Sex (Spring 2006)^ Percetange

Female

Male

Total

26

22

48

Success Rate