1. Stats 2160
Final Project: Is Living Distance Correlated
with GPA?
Katie Cornelius
Victor Jovanovich
Mat Rogers
April 24, 2015
Table of Contents
2. 1
I. Executive Summary 2
II. Introduction 2
III. Methods 3
IV. Analysis 4
V. Conclusions 6
VI. Bibliography 6
Executive Summary
Initially we planned to interview any random sample of students that go to Western
Michigan University. We were looking to find the answer to see if students who live on campus
have a higher GPA than students that live off campus?’ and ‘do students who live in Michigan
have a higher GPA than students that live out of state?’ After our first random selection of
student we found in the library; we collected up to 25 student surveys by the face-to-face
3. 2
method. We asked all the same questions consisting of, Do you live in Michigan? What is your
GPA? Do you live on or off campus? How far away is your hometown from WMU ( in hours)?
After our first analysis, we found we needed to boost our sample size to 100 students to find a
clearer divide among the GPA’s and the distance. We then created our survey sheet to have the
students answer the questions in a more private way. We collected our information in numerous
ways; the Waldo Library, Bernhard center, Friends, and roommates. After the collection of data,
we processed our information through the 2sampleTtest function on the TI-84 calculator, also we
used Microsoft Excel to build the graphs and find our mean and standard deviations of our
GPA’s.
Introduction
We used this project to test the statistics to find if there is a correlation between WMU
students living distance and their GPA. Our population of interest was a random sample of
strictly WMU students. To begin our testing we came up with two categorical variables for our
testing which were ‘Do you live on campus or off campus?’ and ‘Do you live in Michigan or live
out of state?’ We also came up with two numerical variables which were ‘What is your GPA?’
and ‘How many hours away is your hometown from WMU?’ We believe that the closer a
student’s hometown is to WMU and the closer a student lives to campus, the higher the GPA.
The reasoning behind this hypothesis is that the student will be closer to academic resources if
they live on campus. Also we think a student is more likely to attend more classes if they have a
shorter distance to travel to get to class. We think if a student has a hometown closer to WMU
they won’t have to skip out early on classes to accommodate the longer travel time to get back
home.
Methods
4. 3
After collecting the data from the surveys we used it to test our hypothesis. We also put together
an assortment of graphs to help show the differences in our data. For our first graph we stuck
with a traditional bar chart. In the bar chart we are showing the difference in respondents to our
question “Do you live in Michigan?”. We found out of our 100 collected responses we have a
significant difference with 79 students that lived in michigan, 21 students who didn’t; meaning
they left their home state to come to Michigan to study at WMU. The second chart looking
similar to the bar chart is our histogram and in this chart we showed the date of, “How many
hours away do you live from WMU”. To be more clear the question is asking how far away is 0
your hometown from WMU and in this conclusion we also received wide variety of hours.
Ranging from 0 to 7+ hours and resulted in being right skewed. The histogram clearly portrays
and shows the information well. The third graph is our pie chart its showing our information for
the question “ Do you live on or off Campus?”. This was one of our closest charts we got, but
5. 4
overall there were more than half our surveyed students that lived off campus. To display our
results for student’s GPAs, we conducted a stem-and-leaf plot. Out of our sample size of 100,
GPAs ranged from a 2.4-4.0, with a 3.0 being the mode. Students could have said their GPA was
a 3.0 for convenience or for sake of embarrassment of their real GPA, which could have skewed
our results.
Analysis
To begin our testing, we took our 100 completed surveys and entered them into an excel
spreadsheet. We then used excel functions to find the average mean and standard deviation of
GPA of students that live in state and GPA of students that live out of state. We used the same
functions to find the average mean and standard deviation of the GPAs of students that live on
campus and GPAs of students that live off
campus. Once we got the preliminary data
(shown below) needed to perform the
6. 5
2SampTtests we conducted our null and alternative hypothesis as follows:
H0: Average GPA of students in state < Average GPA of student out of state - ✓
HA: Average GPA of Student in state > Average GPA of student out of state - X
2-SampTtest
Live in Michigan Live out of state
x: 3.25 x: 3.18 P-value: .1931 > 0.05 Test stat: .87031
s: .372 s: .382 *do not reject H0, does not shows HA
n: 68 n: 32
H0: Average GPA of student on campus < Average GPA of student off campus -✓
HA: Average GPA of student on campus > Average GPA of student off campus -X
2-SampTtest
Live on campus Live off campus
x: 3.15 x: 3.20 P-value: .7437 > 0.05 Test stat: -
.6571
s: .355 s: .387 *do not reject H0, does not shows HA
7. 6
n: 41 n: 59
For each of our independent sample tests, our P-value was greater than our level of
significance (o.o5). This lead us to not reject H0, and that leads us to not show HA.
Conclusions
—After performing two independent sample tests, we can conclude that we do not have enough
evidence to prove students that live on campus have a higher GPA than students living off
campus. Also we do not have enough evidence to prove that students that live in Michigan have
a higher GPA than students who live out of state. —We believe the sample size of 100 students
was not large enough be be able to show that there is any significant correlation between GPA
and living distance.
Bibliography
- TI-84
- —"Microsoft Excel Online - Work Together on Excel Spreadsheets." Microsoft Excel
Online - Work Together on Excel Spreadsheets. N.p., n.d. Web. 19 Apr. 2015.
- —"Using Excel to Calculate Means and Standard Deviations - Educational Research - Del
Siegle." Using Excel to Calculate Means and Standard Deviations - Educational
Research - Del Siegle. N.p., n.d. Web. 19 Apr. 2015.
