STATS 1202
Introductory Statistics
AY 2023 - 2024, Term 1
Group Project Report: The effects of exercise on BMI
Section: G1
Instructor: Professor Wu Zheng Xiao
Group: 6
Group members
Ryan Ng
See Jinyan
Reyna Seah
Liew Zi Ying
Terence Tan
I.
Executive Summary
According to a report by the National Institute of Health, the beneficial effects of exercise
participation were keeping a normal weight and low BMI.1As university students juggling 5
mods, CCAs and maintaining a healthy study-life balance at the same time, exercise would
more often than not be neglected. Hence, our study aims to determine if the amount of
exercise done by university students will affect their chances of maintaining a healthy weight
and BMI.
We hypothesised that
a. Not exercising results in weight gain and an increase in BMI.
b. Exercising results in weight loss and a decrease in BMI
To test our hypothesis, we surveyed 60 students from sports CCAs in SMU through
convenience sampling. We then subjected each student to certain amounts of exercise over a
duration of 2 weeks, in which the first week no exercise is conducted while in the second
week every individual is to do 30 mins of exercise a day. Afterwards, we used the results to
draw conclusions regarding the 2 variables.
From the results that we have obtained, albeit some anomalies, we have concluded that
a. Not exercising does not result in an increase in BMI
b. Exercising results in a decrease in BMI
II. Introduction
A. Problem
It is important to lead a healthy and active lifestyle, but it is often overlooked by
university students due to their busy schedules. With them being constantly busy, it is
unlikely for many university students to have the time to exercise. As a result, they
are susceptible to living a sedentary lifestyle since they spend the majority of their
time studying and sitting still in school.2 According to the World Health Organization
(WHO), we should inculcate the practice of exercising regularly since it reduces the
associated risks posed by living a sedentary lifestyle.3
1
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7967650/#:~:text=The%20beneficial%20effects%20of
%20exercise,and%20fat%20mass%20%5B8%5D.
2
Physical exercise and body-mass index in young adults: A national survey of Norwegian university
students - Grasdalsmoen, et al. 2019 https://doi.org/10.1186/s12889-019-7650-z Accessed 20 Oct.
2023
3
“Physical Activity - WHO. “
https://www.who.int/news-room/fact-sheets/detail/physical-activity. Accessed 20 Oct. 2023.
1
Fig. 1 Recommended amount of exercise By Different Age Groups
The amount of exercise recommended for university students is 150 minutes of
moderate-intensity activity and at least 2 days a week of activities that strengthen muscles as
seen in Figure 1.4 It is vital for students to stay active in their daily lives given the health
benefits from staying physically active since it improves our brain health and strengthens our
bones and muscles.
B. Choice of Population and Justification
1. Sampling method
A convenience sampling method was used in the research methodology, whereby we
collected the BMI of SMU students from sports CCAs. We intend to generate insights
for quick and straightforward purposes as our respondents are readily available which
saves time and resources.
The population identified consisted of individuals who are SMU students during the
academic year 2023-2024. From the population, we obtained a sample size of 60
students from sports CCAs and subjected them to an experimental study over 2 weeks
and got them to report their data at the end of the experiment.
2. Justification
The rationale behind choosing SMU students as our population (in the approximate
age group between 19-25) in finding the relationship between exercise duration and
BMI as a variable of interest is due to the lack of perceived importance pertaining to
physical activity. According to a 2015 study, 42.1% of university students in
4
"Physical Activity Recommendations - CDC."
https://www.cdc.gov/physicalactivity/basics/pdfs/FrameworkGraphicV9.pdf. Accessed 17 Oct. 2023.
2
Singapore were classified as having ‘low physical activity’ and not meeting the
minimum requirement of walking 30 minutes per day or having a comparable amount
of low and high-intensity activity5. This is further supported by the fact that there is a
decreasing trend of physical activity among them, with many lacking interest in
increasing their physical activity as they are less aware of their physical condition and
do not intend to pursue measures since they perceive that they do not develop
diseases6. Consequently, this may correlate with the idea as to why university students
in Singapore are not pursuing a lifestyle of greater physical activity as advised by the
CDC based on Figure 1.
Our selection criteria for the experiment sample involved exclusively enrolling
students engaged in sports CCAs, a deliberate choice aimed at enhancing the
precision of our findings regarding the influence of exercise on BMI. By instructing
students who maintain a consistent exercise regimen to temporarily cease physical
activity for one week before resuming, we aim to establish a distinct and
demonstrable correlation between exercise and BMI.
C. Our Hypothesis
Our first hypothesis is that no exercise being done results in an increase in BMI. In
2016, an observational study conducted by the UK Biobank showed that people who
do comparatively more physical activity have a lower BMI than less active people7. It
is a common belief that such activities would be the solution to having a healthy
lifestyle and body weight. The research has also asserted the fact that individuals were
associated with a lower BMI and body fat percentage within each category of the BMI
with an average of 1-2% lower than those that are less active. Therefore, we construct
our first hypothesis to test whether this claim is indeed true.
Our second hypothesis is that physical activity lowers an individual’s BMI. According
to a 2012 study by Hall, Klein, Speakman & Kemnitz, exercise programmes are
unlikely to produce weight loss. The researchers have shown that there are other
factors affecting one’s BMI such as calorie intake. Hence, we construct our second
hypothesis to test whether this claim is indeed true.
5
“Physical inactivity and associated factors among university students in 23 low-, middle- and
high-income countries.” - Pengpid, Supa et al. (2015) International journal of public health vol. 60,5
(2015): 539-49. https://pubmed.ncbi.nlm.nih.gov/25926342/
6
Ministry of Health, Labour and Welfare. 2022 National health and nutrition survey.
https://www.mext.go.jp/content/20200324-mxt_kouhou01-000004520_4. Pdf
7
Besson H, Ekelund U, Luan J, et al. A cross-sectional analysis of physical activity and obesity
indicators in European participants of the EPIC-PANACEA study. Int J Obes 2009;33:497–506.
https://bmjopen.bmj.com/content/bmjopen/7/3/e011843.full.pdf
3
III. Data Collection
A. Methodology
This is an experimental study to observe the effect that exercise has on BMI and data
collection was done over a period of 2 weeks. We gathered a group of 60 people from
sports CCAs to take part in our experiment. Each individual would measure their BMI
3 times over the course of the experiment, at the beginning of the experiment (Initial),
after a week with no exercise, and then again after exercising for 1 week. After the
experiment was completed, they would each do an anonymous online survey to
submit their results.
Rationale
Sample: We chose people from sports CCAs in order to better highlight the effects
that exercise has on BMI and because it is generally more feasible to encourage
individuals who were already engaged in physical activity to temporarily pause their
exercise routines than to initiate exercise in those who may not have had a regular
exercise habit.
Measurement: The students will measure their weight when they wake up so as to
minimise water weight and get a more accurate measurement of their weight.
Exercise: All participants will do the same exercise for the same duration to ensure
the experiment is equal and fair.
At the end of our experiment, the data concluded that exercising leads to an overall
decrease in BMI.
B. Collected Data
Initial
After 1st week (no
exercise)
After 2nd week (with exercise)
Sample size
60
60
60
Min
15.24357
15.30924
15.19747
Max
30.95813
31.07721
30.66110
Average
21.47011
21.53760
21.11585
Median
20.63039
20.63145
20.03297
Std dev
4.01452
4.06572
4.00165
Figure 1.1
4
IV. Data Analysis
A. Hypothesis Testing
In our experiment, we will be using two hypothesis tests to determine the accuracy of
our hypothesis. Our hypotheses are:
1. Not exercising increases your BMI
2. Exercising decreases your BMI
1. Hypothesis testing 1
𝐻0 : µ1 = 0
𝐻1 : µ1 > 0
Let µ1 be the mean difference in BMI from their BMI at the end of week 1 to their
initial BMI (Week 1 BMI - Initial BMI), showcasing the effects that not exercising
will have on BMI change.
Since sample size (n=60) is sufficiently large, by CLT, the sample mean is
2
approximately normal. 𝑋 ∼ 𝑁(µ1, σ /𝑛)
At 5% significance level:
Mean BMI of students initially, µ𝑎
21.47011
Mean BMI of students after week 1,µ𝑏
21.53760
Mean difference, 𝐷
0.06749
5.77554
2
∑ (𝐷𝑖 − 𝐷 )
2
Point estimate for population variance, 𝑆𝐷
5.77554
60−1
𝑡𝑠𝑡𝑎𝑡 , where t has (n-1) degrees of freedom
0.06749−0
(
0.09789
60
= 0. 09789
)
= 1. 67088
Using critical value method,
Reject 𝐻0 if 𝑡𝑠𝑡𝑎𝑡 > 𝑡0.05,59= 1.6711
Since 𝑡𝑠𝑡𝑎𝑡 = 1.67088 < 1.6711, we do not reject 𝐻
0
Using p-value method,
Reject 𝐻0 if p-value < 0.05
From the GC, p value = 0.05002 thus p value > 0.05, we do not reject 𝐻0
5
Since 𝑡𝑠𝑡𝑎𝑡 < 1.6711 and p-value > 0.05, we do not reject 𝐻0 and conclude that there is
insufficient evidence showing that there is an increase in mean BMI after not
exercising for a week.
2. Hypothesis testing 2
𝐻0 : µ2 = 0
𝐻1 : µ2 < 0
Let µ2 be the mean difference in BMI change from their week 2 BMI to their BMI at
the end of week 1 (Week 2 BMI - Week 1 BMI), showcasing the effects that exercise
has on BMI.
Since sample size (n=60) is sufficiently large, by CLT, the sample mean is
2
approximately normal. 𝑋 ∼ 𝑁(µ2, σ /𝑛)
At 5% significance level:
Mean BMI of students after week 1, µ𝑐
21.53760
Mean BMI of students after week 2,µ𝑑
21.11585
Mean difference,𝐷
- 0.42175
2.03386
2
∑ (𝐷𝑖 − 𝐷 )
2
Point estimate for population variance, 𝑆𝐷
2.03386
60−1
𝑡𝑠𝑡𝑎𝑡 , where t has (n-1) degrees of freedom
−0.42175−0
(
0.03447
60
= 0. 03447
)
=
− 17. 59709
Using critical value method,
Reject 𝐻0 𝑡𝑠𝑡𝑎𝑡 < - 𝑡0.05,59= -1.6711
Since 𝑡𝑠𝑡𝑎𝑡 = -17.59709 < -1.6711, we reject 𝐻
0
Using p-value method,
Reject 𝐻0 if p-value < 0.05
−25
From the GC, p value = 1.8833 * 10
thus we reject 𝐻0
6
Since 𝑡𝑠𝑡𝑎𝑡 = -17.59709 < -1.6711 and p-value < 0.05, we reject 𝐻0 and conclude that
there is sufficient evidence showing that there is a difference in the mean BMI when
exercise is conducted. In fact, the mean BMI when there is exercise is lower than the
mean BMI without exercise.
Error identified in testing?
The test subjects' BMI may have been affected by several other factors such as their
calorie intake, quality of sleep etc, potentially affecting the results obtained from the
experiment.
V. Conclusion
A. Conclusion on experiments
From our results in the survey, the mean BMI of students after they exercised is lower than
the mean BMI of students before they started the exercise. Hence, we can conclude that
exercise results in a decrease in BMI.
B. Recommendations
Students should exercise more frequently in order to have a greater change in BMI and
maintain a healthy BMI. Considering the results of our experiment, SMU should implement
mandatory exercise programs which focus on cardiovascular and strength training as they are
known to reduce one’s BMI more significantly and keep one fit and healthy. SMU should
also organise special events like field days, sports days, or charity walks/runs to create
excitement around physical activity, encouraging students to exercise.
C. Limitations
The results collected may be affected by some or all of the following factors.
1. Confounding factors present
Some students may naturally maintain their weight and hence, a good BMI without
exercising. This is possible due to their genetics or a healthy and balanced diet as they play
significant roles in one individual's weight and overall health. Furthermore, maintaining a
healthy lifestyle beyond diet alone can help regulate weight. Hence, there are other factors
that can positively affect the BMI of students, affecting the results of our test.
2. Self-Reported Data leading to response bias
Some students who filled out our survey could have a BMI of more than 25 (overweight) and
yet choose to report an inaccurate BMI (less than 25) since they may be ashamed of their
7
weight. This may lead to measurement error in our experiment as they were not truthful in the
survey they participated in.
We recognise the errors during our experiment and have tried to minimise them. Take for
instance, the identities of the participants are kept anonymous and we do not require them to
submit their names during our survey so that they would be more truthful when answering the
questions. This ensures that our survey results are accurate and reliable.
VI. Appendix
A. Survey Questions
1) What is your initial BMI (to 5 d.p.) before exercise?
2) What is your BMI after 1 (to 5 d.p.) week of not exercising?
3) What is your BMI after 1 (to 5 d.p.) week of exercise?
The BMIs are computed based on kg/m².
B. Raw data of our participants
Initial BMI before exercise
After 1 week no exercise
after 1 week of exercise
17.28673
17.30947
17.37253
15.70316
15.30924
15.19747
18.18584
18.50140
18.36375
30.67827
30.78285
30.26438
28.01186
27.58686
27.04553
25.33733
25.32435
24.94765
25.55991
25.86061
25.48049
15.24357
15.41750
15.25399
27.07148
27.20479
26.66800
28.53384
28.36509
28.01491
27.28719
27.76991
27.22067
27.20393
27.42605
26.82959
17.56345
17.62821
17.48651
20.97782
21.11424
20.65519
28.63415
28.50029
28.06047
24.40618
24.50373
23.97201
15.85334
15.94661
15.96531
20.87043
21.21282
21.09617
28.42972
28.51703
28.14290
8
22.46652
21.96304
21.27279
17.78765
17.79232
17.65487
17.25269
16.89750
16.50055
22.98474
22.98333
22.41463
17.72609
17.44965
17.27814
18.88290
18.38868
17.99215
20.52388
20.03533
19.46714
18.01498
17.38618
17.47455
27.54065
27.87370
27.52865
20.92970
20.79674
20.33681
18.45812
18.19596
17.77909
17.89315
17.48741
16.83342
19.97456
19.50673
19.10028
20.45506
19.87786
19.39343
17.92222
18.01266
17.62602
18.81327
19.39693
18.78375
22.13285
22.57236
22.11896
17.21201
17.51073
17.13825
20.95316
21.53804
20.95822
22.94572
23.10328
22.76694
30.95813
31.07721
30.66110
18.55229
18.78752
18.19164
26.06455
26.10693
25.51500
18.46593
18.60268
18.29121
24.19471
24.39304
23.86396
21.10081
21.11170
20.56303
19.00669
19.57938
19.18685
18.20728
18.26793
17.74375
19.32584
19.65354
18.95786
22.99929
23.54818
22.99192
17.77641
18.08354
17.62097
18.67398
18.94863
18.52628
22.57196
22.63570
22.17424
17.44096
17.45848
17.00956
21.88387
22.24466
21.81786
19.85619
20.15238
19.49672
9
C. BMI Table for men and women
Fig. 28 BMI Table for men and women
Figure 1.2 (Initial week)
8
"BMI Chart For Men And Women – Forbes Health." 1 Jun. 2023,
https://www.forbes.com/health/body/bmi-chart-for-men-and-women/. Accessed 25 Oct. 2023.
10
Figure 1.3 (After 1st week)
Figure 1.4 (After 2nd week)
11