Yo, I'm Tired.
A study of levels of rest teenagers get
by Christina Huang and Mei Ling Xu
by Christina Huang and Mei Ling Xu
Overview
Have you ever felt so tired that you couldn't tell if you were awake or having a bad dream? Unfortunately, this is the kind of experience that teenagers face daily. With the need to balance academics, extracurriculars, part-time jobs, volunteer work, social life, along with physical and mental health, teenagers find that they have to sacrifice precious sleep time in order to accomplish their goals and become a "well-rounded" student. This study is important because teenagers today face an epidemic of physical and mental health. Students often place their academic goals higher than their own health and wellbeing on their list of priorities. This has become a serious issue. And very visible in the lethargic, glazed over look in the eyes of today's high school students. In this study, we surveyed a group of students at Boston Latin School about their daily activities and the amount of rest they get. We asked the following questions and recorded their answers:
Below is the recorded data from these questions:
Have you ever felt so tired that you couldn't tell if you were awake or having a bad dream? Unfortunately, this is the kind of experience that teenagers face daily. With the need to balance academics, extracurriculars, part-time jobs, volunteer work, social life, along with physical and mental health, teenagers find that they have to sacrifice precious sleep time in order to accomplish their goals and become a "well-rounded" student. This study is important because teenagers today face an epidemic of physical and mental health. Students often place their academic goals higher than their own health and wellbeing on their list of priorities. This has become a serious issue. And very visible in the lethargic, glazed over look in the eyes of today's high school students. In this study, we surveyed a group of students at Boston Latin School about their daily activities and the amount of rest they get. We asked the following questions and recorded their answers:
- Male or female?
- On a scale of 1-10, 1 being the most tired, how rested do you feel throughout the day?
- How many hours of sleep do you usually get?
- How many hours of intense exercise do you usually do per day?
- How many hours do you usually spend studying per day?
- How many hours do you usually spend on media per day?
- Would you say you usually have a small, medium or large breakfast every day?
- Would you say you usually have a small, medium or large lunch every day?
- Would you say you usually have a small, medium or large dinner every day?
Below is the recorded data from these questions:
Questions:
1. If titled “A Good Rest Includes What?” what is/are the independent variable(s) of this experiment?
The independent variables would be hours of sleep, media, studying, eating portions,and gender, because the level of restedness depends on these variables.
2. What is the dependent variable for the title in question 1?
The only dependent variable is feeling of restedness (1-10).
3. Create a scatter plot with rested vs. sleep. What kind of correlation do they have?
1. If titled “A Good Rest Includes What?” what is/are the independent variable(s) of this experiment?
The independent variables would be hours of sleep, media, studying, eating portions,and gender, because the level of restedness depends on these variables.
2. What is the dependent variable for the title in question 1?
The only dependent variable is feeling of restedness (1-10).
3. Create a scatter plot with rested vs. sleep. What kind of correlation do they have?
The graph shows a positive correlation, such that the more hours students sleep, the more rested they feel.
4. What is the mean number of hours for sleep?
10(6)+5+7+7+6.5+5+4+5+5.5+9+5+3.5+6+5= 135.5/23 =5.9
The mean hours for sleep is 5.9 hours.
5. Create a scatter plot with rested vs. studying. What kind of correlation do they have?
10(6)+5+7+7+6.5+5+4+5+5.5+9+5+3.5+6+5= 135.5/23 =5.9
The mean hours for sleep is 5.9 hours.
5. Create a scatter plot with rested vs. studying. What kind of correlation do they have?
The graph shows no correlation between the hours a student studies and how rested they feel, because the points are all scattered with no patterns.
6. What percentage of students feel rested at a 5 or above and eat a medium lunch?
There are 24 students who answered the survey. 8 of them usually eat medium lunches and feel rested at a level 5 or more on a 1 to 10 scale.
8/24=.33
33% of students feel rested at a 5 or above and eat a medium sized lunch.
7.Prove whether or not people exercise the same amount of time they study.
a) Write out the hypothesis.
H0: μ=0
Ha: μ≠0
b) What is the sample mean diff of the data?
There are 24 students who answered the survey. 8 of them usually eat medium lunches and feel rested at a level 5 or more on a 1 to 10 scale.
8/24=.33
33% of students feel rested at a 5 or above and eat a medium sized lunch.
7.Prove whether or not people exercise the same amount of time they study.
a) Write out the hypothesis.
H0: μ=0
Ha: μ≠0
b) What is the sample mean diff of the data?
Using the calculator, set "int.ex" as L1 and "studying" as L2, then L1 - L2 as L3. Put STAT, then move to 2nd tab called CALC, and enter 1-Var Stats and enter L3, so it would look like 1-Var Stats L3.
It shows that x-bar is .11.
It shows that x-bar is .11.
c) What is the standard deviation of the sample?
Sx=1.0
d) What is the test statistic?
t=(x-bar - μ0)/(Sx/√n)t=(.11-0)/(1.0/√23)=.53
e)what is the p-value?
Using the calculator, click 2ND, then VARS, and enter tcdf(.53, 1000000, 22), which is .30, but since it is μ≠0, then you must multiply by 2.
The p-value is .60.
f) If the significant figure is .05, then what is the conclusion?
Since we fail to reject the null hypothesis, then there must be a difference between amount of time spent studying and exercising.
8. What is the margin of error for problem 7 above if 95% confident?
n=23
x-bar=.11
Sx=1.02
t at 95%=2.064
M. E.=(2.064)(1.02/√23)=.44 The margin of error is .44.
a) What is the confidence interval for 95%?
(.11-.44,.11+.44)= (-.33, .55)
9. What percent of the people eat a large dinner, given that they have a small breakfast?
There are 17 students who usually eat small breakfasts, and 12 of the 17 eat large sized dinners.
12/17= .71
71% of students usually large dinners given that they eat small breakfasts.
10. What percent of the people eat a medium lunch, given that they have a small breakfast?
There are 17 people who eat small breakfasts and 7 of them eat medium lunches.
7/17=.41
41% of students usually eat medium lunches given that they eat small breakfasts.
Sx=1.0
d) What is the test statistic?
t=(x-bar - μ0)/(Sx/√n)t=(.11-0)/(1.0/√23)=.53
e)what is the p-value?
Using the calculator, click 2ND, then VARS, and enter tcdf(.53, 1000000, 22), which is .30, but since it is μ≠0, then you must multiply by 2.
The p-value is .60.
f) If the significant figure is .05, then what is the conclusion?
Since we fail to reject the null hypothesis, then there must be a difference between amount of time spent studying and exercising.
8. What is the margin of error for problem 7 above if 95% confident?
n=23
x-bar=.11
Sx=1.02
t at 95%=2.064
M. E.=(2.064)(1.02/√23)=.44 The margin of error is .44.
a) What is the confidence interval for 95%?
(.11-.44,.11+.44)= (-.33, .55)
9. What percent of the people eat a large dinner, given that they have a small breakfast?
There are 17 students who usually eat small breakfasts, and 12 of the 17 eat large sized dinners.
12/17= .71
71% of students usually large dinners given that they eat small breakfasts.
10. What percent of the people eat a medium lunch, given that they have a small breakfast?
There are 17 people who eat small breakfasts and 7 of them eat medium lunches.
7/17=.41
41% of students usually eat medium lunches given that they eat small breakfasts.
Citations:
image above; http://www.eduinreview.com/blog/2010/08/how-sleep-learning-may-improve-your-grades/
image above; http://www.eduinreview.com/blog/2010/08/how-sleep-learning-may-improve-your-grades/