End of Semester Project - TEMPLATE - updated for Fall 2023 (1)
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Mathematics
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Nov 24, 2024
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Name: Aruna Bakarr
MAT152 End of Semester Project TEMPLATE
You will complete this project using the data and analysis from your Mid-semester Project. Please refer to the End of
Semester Project Example that has directions and tips to guide you as you reflect on your project and provide answers for
each question based on the data you gathered.
Question 1:
What study did you conduct for your mid-semester project and what were the results? Did you make any
adjustments from your mid-semester data that will be discussed moving forward?
Directions:
Summarize your findings from your previous project (Mid-Semester Project: Units 1 and 2). Include what
your question was, what the results were, and any other pertinent information.
Population: American adults aged 18-40.
Numerical Question: On average, how many days do you engage in physical activity per week?
Non-Numerical Question: What sorts of emotional or psychological benefits you have experienced as a result of
regular physical activity
Data Collection:
•
Online survey
•
Sample size: 40 individuals
•
Age range: 18-40 years
Findings:
•
Average number of days American adults aged 18-40 engage in physical activity per week: 4.4 days
•
Median number of days American adults aged 18-40 engage in physical activity per week: 5 days
•
Age distribution in the sample: relatively even, with a slight skew towards more participants in their 20s
•
Psychological benefits of physical activity:
*
Unspecified benefits (25%)
*
Enhanced self-esteem (22%)
*
Stress reduction (15%)
*
Increased energy (13%)
*
Anxiety management (10%)
*
Better sleep quality (10%)
*
Sense of accomplishment (5%)
Adjustments to Data:
•
Removed outliers from the age distribution
•
Adjusted the categorization of the non-numerical question to include "Other"
Additional Findings:
•
The sample size is relatively small and may not adequately represent the diverse population of American adults
aged 18-40.
•
A random sample would be more representative of the population.
•
Stratified sampling for demographics like age, gender, and ethnicity could enhance representativeness.
Conclusion:
Name: Aruna Bakarr
The findings suggest that American adults aged 18-40 engage in physical activity for an average of 4.4 days per week.
The majority of respondents reported unspecified benefits from physical activity, followed by enhanced self-esteem
and stress reduction. These findings provide valuable insights into the physical activity habits and psychological
benefits experienced by this specific age group.
Question 2:
What information did you collect from participants? Was your information categorical or quantitative?
Explain your answer(s).
Directions:
Revisit the data you collected from participants. Explore the concepts of categorical and quantitative data
and apply them to each variable you collected.
Age
: Participants' ages are measured in years and can take on any numerical value within the specified range (18-40
years). This makes age a quantitative variable.
Days of physical activity per week:
The number of days’ participants engage in physical activity per week is also a
quantitative variable. It can take on any integer value between 0 and 7.
Psychological benefits:
The types of psychological benefits participants experience from physical activity are categorical.
Participants can only select one benefits from a predefined list of options ("stress reduction," "anxiety management,"
"enhanced self-esteem," "better sleep," "increased energy," "sense of accomplishment," and "other").
Question 3:
Does there appear to be any correlation between age and the question you asked?
You must support
your answer by creating a scatter plot and running a linear regression on Excel or
alcula.com
.
If so, is the correlation
positive or negative?
Explain in a minimum of 2 sentences, and you MUST include a picture of your scatter plot.
15
20
25
30
35
40
45
0
1
2
3
4
5
6
7
8
f(x) = 0.05 x + 2.92
R² = 0.04
Days of Physical activity per week versus Age
Days of Physical activity per week
Age
Name: Aruna Bakarr
There appears to be a weak positive correlation between age and the days of physical activity per week. This means that as
age increases, the number of days of physical activity per week also tends to increase. The correlation coefficient is
0.1901, which signify a very weak correlation.
Question 4:
After constructing a linear regression of the data, answer the following questions.
a.
What is the equation of the trendline?
The equation of the trendline is y = 0.0525x + 2.9228.
b.
What is the coefficient of determination (R
2
)?
The coefficient of determination (R- square) is 0.0361. This means that 3.61% of the variation in days of physical
activity per week can be explained by the variation in age.
c.
Write a contextualized summary about the slope, y-intercept, and coefficient of determination. Include whether
the data makes sense in the real-world context.
Slope: The slope of 0.0525 indicates that for every one-year increase in age, there is an expected increase of
0.0525 days of physical activity per week.
Y-intercept: The y-intercept of the trendline is 2.9228. This suggests that even younger adults are likely to engage
in some physical activity, with the average being 2.9228 days per week.
The coefficient of determination (R- Square) is 0.0361, indicating that only 3.61% of the variation in days of
physical activity per week can be explained by the variation in age.
Overall, the data makes sense in the real-world context, as it reflects the complex interplay of factors that
influence physical activity levels.This makes sense in the real-world context, as there are many other factors that
can influence physical activity levels, such as health status, lifestyle choices, and access to opportunities for
physical activity. Therefore, it is not surprising that age only explains a small portion of the variation in physical
activity levels among adults aged 18-40.
Question 5:
Was your study an observational or an experimental study? State whether your study was observational or
experimental and explain.
Directions:
Discuss whether your experiment was observational or experimental.
My study was an observational study. Observational studies are those in which the researcher observes and records the
behavior of participants without manipulating any variables. In my study, I collected data on the physical activity habits
and psychological benefits experienced by a sample of American adults aged 18-40. I did not manipulate any variables,
but simply observed and recorded the participants' responses to my survey questions.
Question 6:
What were the limitations of the study you conducted?
Directions:
Consider what you know about statistical studies and their limitations. Evaluate the limitations of your
statistical study.
The following are the limitations of the study I conducted:
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Name: Aruna Bakarr
The sample size was relatively small, which may not adequately represent the diverse population of American adults aged
18-40.
The study was conducted online, which may have excluded individuals who do not have internet access or who are not
comfortable using online surveys.
The study was self-reported, which means that participants may have overestimated or underestimated their physical
activity levels or the psychological benefits they experienced.
The study was cross-sectional, which means that it cannot determine cause-and-effect relationships between age, physical
activity levels, and psychological benefits.
In the future, the study could be improved by using a larger sample, diverse participants, alternative data collection
methods, and a longitudinal design.
Question 7:
Answer the following questions after considering the possible bias(es) that are present in your statistical
study.
Directions:
Discuss what you did to avoid or minimize bias in your study.
Note: Every study most likely has some
sort of bias.
a.
What did you do to avoid or minimize bias in your study?
To minimize bias, I used an online survey for data collection, allowing participants to respond independently.
However, convenience sampling introduced selection bias, as participants were drawn from my immediate
network.
b.
Which bias(es) occurred in your study?
Selection bias occurred due to the non-random sampling method, potentially leading to results that may not be
generalizable to the broader population.
c.
How could you minimize this bias in future studies?
Future studies could employ random sampling methods, ensuring a more representative and diverse participant
pool, and increasing the external validity of the findings. Additionally, using stratified sampling based on
demographics would address potential biases related to participant characteristics.
Name: Aruna Bakarr
Question 8:
If you were to expand your study to 500 people, what could you expect your categorical (non-numerical)
results to look like? In other words, how many people out of 500 would have given each of your responses. *Assume your
results would be proportional to your original study.*
Directions:
Apply your knowledge of proportional reasoning to expand your study. Imagine you wanted to ask 500
people your question(s). Determine the approximate number of individuals that would have responded in particular ways
using proportional reasoning.
a.
Support your answer with work; make sure to turn this in or represent this in your project.
Give specific numbers.
Type of Benefits
Frequency
Anxiety management
4
Better Sleep
4
Enhanced Self-Esteem
9
Increased Energy
5
Other
10
Sense of Accomplishment
2
Stress Reduction
6
Grand Total
40
Now, for the expansion of the study from 40 to 500 people:
Anxiety Management: 4 out of 40 people reported experiencing this benefit from physical activity.
4
40
=
x
500
x
=
4
40
×
500
x
=
50
Better Sleep: Similarly, 4 out of 40 people reported experiencing better sleep.
4
40
=
x
500
x
=
4
40
×
500
x
=
50
Enhanced Self-Esteem: 9 out of 40 people reported experiencing enhanced self-esteem.
9
40
=
x
500
Name: Aruna Bakarr
x
=
9
40
×
500
x
=
112.5
≈
113
Increased Energy: 5 out of 40 people reported increased energy.
5
40
=
x
500
x
=
5
40
×
500
x
=
62
.
5
≈
63
Other Benefits: 10 out of 40 people reported experiencing other benefits.
10
40
=
x
500
x
=
10
40
×
500
x
=
125
Sense of Accomplishment: 2 out of 40 people reported a sense of accomplishment.
2
40
=
x
500
x
=
2
40
×
500
x
=
25
Stress Reduction: 6 out of 40 people reported stress reduction.
6
40
=
x
500
x
=
6
40
×
500
x
=
75
b.
Write a contextualized sentence(s) explaining your results.
Expanding the study to 500 people, the expected distribution remains proportional to the original sample, with
around 50 reporting anxiety management and better sleep, approximately 113 reporting enhanced self-esteem,
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about 63 reporting increased energy, 125 reporting other benefits, 25 reporting a sense of accomplishment, and 75
reporting stress reduction.
Question 9:
Which study would you expect to be more reliable - your initial study or a study that was conducted with 500
people? Explain your reasoning.
A study conducted with 500 people is expected to be more reliable due to its larger and more diverse sample, minimizing
the influence of random fluctuations seen in smaller studies and enhancing the overall credibility of the results.
Question 10:
Time to wrap things up! Highlight key points from your study and why you decided to ask this question.
You should address at least 3
of the prompts below.
Directions:
Write a conclusion summarizing your study and what you learned. Highlight key information and
anything you found particularly interesting.
Prompts to consider:
o
What questions did you ask and why did you ask them (why are they interesting to you)?
o
Were you surprised by the information you received from participants? Explain.
o
Comparing this project to your mid-semester project, what are some things you have learned, gotten
better at, or strengthened your understanding of?
o
What did you find interesting about this project? Give specific details.
o
“In the future I would…”
o
“What I will be taking away from this project is…”
In this study, I asked questions about physical activity habits and psychological benefits among American adults aged 18-
40. I found these questions interesting as they shed light on the varied experiences and perceptions of individuals. The
participants' responses, particularly on psychological benefits, were intriguing, and I learned the importance of a larger
sample size for a more reliable study. Compared to the mid-semester project, I improved my data interpretation skills and
gained insights into the complexities of studying human behaviors. In the future, I would aim for larger and more diverse
samples to enhance the generalizability of findings. What I'm taking away is a deeper understanding of research nuances
and the significance of thoughtful question formulation.