Sleep Activity Statistics (Coursework Sample)

Stat 1400 Lab 6
Normal Distribution - Amount of Sleep
Do we humans get enough amount of sleep we need?
Here is what some experts are saying...
"There is increasing evidence that there is a very strong relationship between sleep quality and physical and mental health..." A national survey of 31,044 adults revealed a link between insomnia and other sleeping problems with high blood pressure, heart failure, anxiety, and depression. Experts say that there is no evidence yet to indicate that acquiring more sleep will improve medical conditions, but some studies have shown that more sleep makes teenagers do better in school.
The US National Sleep Foundation suggests that an adult needs seven to nine hours of sleep a night. The Foundation conducted a survey in 2012 that suggested about 75% of Americans had sleeping problems, with one-third being so sleepy during the day that it affected their lives and activities.
* What is the implied population?
The implied population is the totality of the American population.
* What is the sample?
The sample is the 31,044 American adults who participated in the national sleep survey.
* Is 75% a statistic or a parameter? Explain.
It is a parameter because it is concerned with the population.
On the other hand, when asked if everyone needed 8 hours of sleep each night, some experts stated: "It's nonsense. It's like saying everybody should have size eight shoes, or should wear Medium size clothes... However, the amount of sleep is normally distributed with the average amount of sleep equal to seven and a quarter hours." Many people report their amount of sleep to be more or less than the average. Experts say that the determining factor for the required amount of sleep should be whether the person feels fresh and alert during the day.
While amount or quality of sleep undergoes a wide variety of changes during the human life span (based primarily upon age and life style), the amount of sleep, at any given age, has a relatively normal, bell-shaped distribution.
We will use this information to explore your sleep habits. First you need to collect a small data set. Record, to the nearest quarter of an hour, how many hours you slept in the past 24 hours.
7 hours and 45 minutes (7.75~ 8 hours)
* Ask 3 more adults (i.e. your team members or other classmates) how many hours of sleep they got in the past 24 hours and record their answers here to the nearest quarter of an hour.
Average hours of sleep

Subject 1

Subject 2

Subject 3


7:30

6:30

5:00

* Use the information presented at the beginning of this activity (specifically that the amount of sleep your data set and the results of the following survey to answer the questions that follow:
SURVEY: A previous study administered to US adults showed that the amount of sleep (in hours)they get in a 24-hour period is normally distributed with a mean of 7 hours and a standard deviation of 1.25 hours. SURVEY: A previous study administered to US adults showed that the amount of sleep (in hours)they get in a 24-hour period is normally distributed with a mean of 7 hours and a standard deviation of 1.25 hours.
Questions:
1 What percent of adults from the survey slept longer than you did?
Z=x-μσ=8-7.001.25=0.8
PZ≤0.8=0.7881
Px>8=1-Px≤8=1-0.7881=0.2119
Thus, the percentage of adults who slept longer than I did is 21.19%.
2 How long did the person who slept the least in your data set (other than you) sleep? What percent of adults from the survey slept less than this person?
Subject 3 slept for the least amount of time (5.00 hours).
Z=x-μσ=5.00-7.001.25=-1.6
PZ≥-1.6=Px<5.00=0.05480
Thus, the percentage of adults who slept less than the person who slept the least is 5.48%.
3 How long did the person who slept the most in your data set (other than you) sleep? What percent of adults from the survey slept more than this person?
Subject 1 slept for the least amount of time (7.50 hours).
Z=x-μσ=7.5-7.001.25=0.4
PZ≤0.4=0.6554
Px>7.50=1-PZ≤0.4=1-0.6554=0.3446
Thus, the percentage of adults who slept more than the person who slept th