To Determine If Sleep or Lack of Sleep Can Cause Obesity Among University Students

Statistics Project
MATH 2014

Prepared for:
Sylvester Phagoo

Prepared by:
Denille Layne # 55937

Coursework Title:
To determine if sleep or a lack of sleep can cause obesity among University students
Introduction:

The question in front of physicians now is “can sleep or the lack of sleep cause obesity?” recent research findings say yes, but is it true? They say that a lack of sleep makes you gain fat. Sleeping less can cause changes in complex metabolic pathways that control your appetite, food intake and energy expenditure. But are they correct?
I have chosen the topic, the relationship of the number of hours of sleep and weight because I want to falsify the claim that we tend to gain weight or be heavier if we would sleep less. I think people should lose weight since we use less energy when sleeping and we tend to use more energy when awake. I conducted the research to know if the claim is really true or not.
I also used university students as my sample population because in today’s society, when students enter into university there is an academic and personal transition that can sometimes cause an imbalance in regular eating and sleeping habits. Objective:

This research aims to falsify the claims that if you would sleep less, you would gain weight, and you would lose weight if you would sleep more. It also aims at knowing the real effect of sleep to the weight of students attending a sample university
Data Collection:

This research covers the weight and number of hours of sleep of 50 first and second year Diploma students from the University of Trinidad and Tobago. This research is limited to UTT students only with ages ranging from 18-24
Population description: This project entailed that the survey be conducted amongst two significant groups, a year 1 diploma population and a year 2 diploma population. The year 1 diploma population would be individuals of the University of Trinidad and Tobago of all ages, and gender. The year 2 diploma students would also be individuals of University of Trinidad and Tobago of all ages, and gender. Each individual would be randomly selected via a specific process detailed below.
Sample description: This survey involved two samples, one sample of 25 individuals who were each randomly selected from year 1 Diploma at UTT and another sample of 25 individuals who were randomly selected from year 2 Diploma at UTT. Each actual population is greater than 200 supporting the independence of the survey.
Sample selection process: Two separate populations would be obtained using two lists; one, a list of year 1 diploma students and the other, a list of year 2 diploma students form the faculty advisors at the University. For each separate group the following process was performed once: This sample, one that is a simple random sample because each of the individuals involved have an equal chance of being selected and are not divided into particular blocking of characteristics within their own population. So in using the list, all individuals were alphabetized by first name and given a number from 000-200. Each individual was then randomly selected for the consistent sample size of 25 individuals. A random digit generator program on a scientific calculator (provided by a lecturer) was used to help randomly choose the sample size numbers. Entering the correct key strokes, the numbers 000-200 were generated randomly, and with each generated number the first twenty-five numbers which corresponded to an individual was the individual selected for the study and any repetition was disregarded.
Study Process: The following was also performed twice, once for each sample: The selected individuals of the sample were placed in a room and given the survey to complete. Selected individuals then took a few minutes of their time to answer the multiple choice questions and then dropped the survey in a box provided. In this system, each individual’s response remained anonymous. Then the results of the survey were each organized by question and by the number of individuals who answered the particular answer choice. Those statistics and data table information were then analysed in the form of graphs and graph comparisons.

Raw Data:

Sample Data Name | Weight (kg) | Average number hours of sleep (hours) | Alex Ayoung | 73 | 6 | Ana Karenina | 96 | 4 | Ariya Surijbally | 42 | 6 | Cataleya Singh | 43 | 5 | Christian Mendez | 50 | 8 | Denille Layne | 60 | 5 | Dray Singh | 71 | 9 | Eric Banner | 51 | 7 | Gloria Hastings | 73 | 5 | Jason Maraz | 67 | 7 |

Table 1: Table 1 displays a sample taken from the data collected. It shows the weight and the corresponding average number of hours of sleep of the year 1 diploma students.

Name | Weight (kg) | Average number hours of sleep (hours) | Jason Samuel | 51 | 8 | Jessica Cruz | 68 | 6 | Joel Ramsden | 73 | 7 | Luis Melendez | 78 | 8 | Maria Rampaul | 45 | 5 | Micheal Manwaring | 72 | 6 | Omar Al Adin | 59 | 5 | Stephen Ramsumir | 86 | 8 | Tobi Mohammed | 67 | 7 | Trent Goodman | 64 | 8 |

Table 2: Table 2 also displays a sample taken form the data collected and it shows the weight and corresponding average number of hours of sleep of the year 2 diploma students

Although the data looks quite scattered in the tables, you can tell that those who weighed less had very little amount of sleep on average. However it should be taken into consideration that some students claimed to have a lot of homework and that resulted in less sleep.

Data Presentation:

Figure 1 shows the relationship between the number of hours of sleep and weight of students in year 1 diploma at UTT.

Figure 2 shows the relationship between the number of hours of sleep and weight of students in year 2 diploma at UTT

Data Analysis:

Standard Deviation
Standard deviation is a formula which measures the dispersal of the data. In this investigation I wanted to find the dispersal of the data found between the weight of student and the amount of sleep.

Calculation of standard deviation for year 1 diploma
Sx= x2n-x2 Sy= y2n-y2

Where: x2 = 1015 x = xn = 15525 = 6.2
N = 25
Sx= 101525-6.22 = 1.469 = 1.5

y2 = 105461 y = 63.4
N =25
Sy= 10546125-63.42 = 14.1024 = 14.1

Table 3: Year 1 Diploma | Mean | Standard Deviation | N | No. of Hours of Sleep | 6.2 | 1.5 | 25 | Weight | 63.4 | 14.1 | 25 |

The average number of hours of sleep of the students is 6.2 hours
However it normally deviates by 1.5 hours
The average weight of students is 63.4 kg. However it normally deviated by 14.1 kg

Calculation of standard deviation for year 2 diploma
Sx= x2n-x2 Sy= y2n-y2

Where: x2 = 1109 x = xn = 16325 = 6.52
N = 25
Sx= 110925-6.522 = 1.36

y2 = 101944 y = 62.8
N =25
Sy= 10194425-62.8 = 11.57

Table 4: Year 2 Diploma | Mean | Standard Deviation | N | No. of Hours of Sleep | 6.52 | 1.36 | 25 | Weight | 62.8 | 11.57 | 25 |

The average number of hours of sleep of the student is 6.52 hours
However it normally deviates by 1.36 hours
The average weight of students is 62.8 kg. However it is normally deviated by 11.57 kg

Regression
The regression formula calculates the relationship between x and y in the form of a line equation. This line equation is in y intercept form when completed and can be fitted on the scatter plot graph as a line of best fit.
Calculating Regression for year 1 diploma y- y=b ( x- x)

Where b = SxySxx
Sxx = 2.16
Sxy = xyn- x×y
= 993025- 6.2 ×63.4 = 4.12 Therefore b = 4.12/2.16 = 1.9
And
y- 63.4=1.9 ( x- 6.2) y=1.9+51.62 Is the regression line and can be used as the line of best fit in figure 1
Calculating Regression for year 2 diploma y- y=b ( x- x)

Where b = SxySxx
Sxx = 1.8496
Sxy = xyn- x×y
= 1041325- 6.52 ×62.8 = 7.064 Therefore b = 7.064/1.8496 = 3.82
And
y- 63.4=1.9 ( x- 6.2 ) y= 3.82x+37.9 Is the regression line and can be used as the line of best fit in figure 2

Product Moment Correlation Coefficient
This equation is useful when you want to find how relative the data of your two variables are

Finding r for year 1 diploma r= Sxy Sx Sy r= 4.12 1.469 ×14.1024 = 0.199

Finding r for year 1 diploma r= Sxy Sx Sy r= 7.0641.36 ×11.57 = 0.449

Figure 3 Same Scatter plot graph as in figure 1, however this one contains the line of best fit.

Figure 4 Same Scatter plot graph as in figure 2, however this one contains the line of best fit.

Figure 3 and 4 are the same scatter plot with a line of best fit. As you can see, the equations above gave me the y intercept formula. The line has a negligible positive linear correlation.

Result:

The graph in figure 1 and figure 2 shows a scatter plot graph with all the data from the 50 students, figure 3 and figure 4 are the same graphs but this time they have a line of best fit. The line of best fit was found with the regression. The line demonstrated was a positive linear correlation, between the number of hours of sleep and weight of year 1 and year 2 diploma students at the University of Trinidad and Tobago, which was almost flat. This demonstrates strong trends and almost neutral data. Therefore we could say that whenever the number of hours of sleep would increase there would be a low chance that their weight would also increase. Furthermore the standard deviation test showed and supported that the variables were compact and sufficient data.

Limitations:
There were a few limitation in my in my investigation. Firstly I survey 50 students from an overall population greater than 200. Although I attempted to make the survey fair and survey students of every age and gender, the data would have been more accurate if all 200 plus students were surveyed.
Another limitation is that, my sample population was University students and some of the students had homework, assignments and quizzes, which prevented them from sleeping like they would normally.

Conclusion:
Although there were limitations that made my data less accurate than was expected. I believe that I received an answer from my studies. According to my theory, as the x axis increases there is a very low chance that the y would also increase. My line of best fit does technically fit this theory, however the strength if the line isn’t as strong as I would like it to be. If I had asked a completely different group of 50 students, there could be a chance that my line went level with no relation. However I believe that if the entire of the year1 and year 2 diploma students in the University were surveyed, the relationship of the data could have strengthened. In other words the line of best fit would have turned into a more positive slope. In conclusion the less you sleep does not necessarily mean that you would gain weight and you sleep more, it does not mean you would lose weight.

Summary of my Project

Researchers | Me | Weight
Weight
Sleep
Sleep
As sleep decreases weight increases Weight
Weight
Sleep
Sleep
As sleep increases weight decreases | Weight
Weight
Sleep
Sleep
I think what the researchers are saying is not necessarily true. After I conducted my research I think as (x) sleep decreases, your weight (y) would decrease. Also I think that you weighty should decrease when you sleep less because you burn more energy while you are awake. |
Recommendation

I would like to recommend to everyone concerned that we need to consider the results of this research that there is a relationship that exists between the number of hours of sleep of a person to his/her weight. This means that sleeping less could affect your weight so I would like to recommend that everyone should at least sleep for about an average of 8 hours per day. Losing weight from lack of sleep is not a good thing, if you want to lose weight you should exercise, but always keep your sleep at about the average or normal sleeping time for an adult/ adolescent. Sleep less could also be the cause of sleep deprivation, and as much as possible you should try to avoid it. Manage your time wisely and have a good sleeping habit.