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Application Project: Part 1
MATH 216
03-25-2008
Student Sleep and GPA Studies
Recent findings have shown that sleep plays an important role in learning processes and
memory consolidation for students of all ages. These studies clearly display that sleep deprivation in
students can impair learning and memory, affecting academic performance. It was noted that college
students who exhibited more regular sleep-wake patterns, represented by earlier sleep times, shorter
times to fall asleep, fewer night awakenings, later school rise times, and earlier rise times on weekends,
reported higher mean GPAs. Conversely students with lower grades reported increased daytime
sleepiness, more frequent night waking, and longer times to fall asleep.
An article, “Sleep Loss, Learning Capacity, and Academic Performance” from Sleep Medicine
Reviews, reports on a study in which surveys were administered to first-year college students. The
researchers observed that sleep habits were highly correlated with academic performance. The official
grades, which were provided by the university registrar, showed that students with lower GPAs were
those with later bedtimes and rise times on both weekdays and weekend days. The authors proposed
that, for each hour less then the average sleep time during the week, the predicted GPAs could decrease
by 0.13 on a scale of 0–4. The authors suggested that this sleep reduction could induce a diminished
ability to recall complex material learned earlier in class.
Another study, as reported in the College Student Journal, “The Relationship between Sleep
Length and Grade-point Average among College Students” mentions a sleep vs. GPA analysis which was
conducted on a total of 148 undergraduate students who had volunteered for the study. Short sleepers
were defined as those who reported sleeping an average of 6 or fewer hours per night. Average sleepers
would spend 7-8 hours per night sleeping. Long sleepers were those who reported sleeping 9 or more
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hours per night. The data collected showed that a total of 23 (15.5%) of the participants qualified as
short sleepers; 107 (72.3%) as average sleepers; and 18 (12.2%) as long sleepers. While the factors of
age and gender did not correlate with GPA, long sleepers reported a GPA (mean = 3.24) significantly
higher than short sleepers (mean 2.74). While average sleepers (mean = 3.01) were not significantly
different from long or short sleepers.
For this application project, we propose to gather data from our current Math 216 class
concerning the sleep versus GPA of Vanderbilt Engineering students. For the purpose of the study, we
will assume that the students in this class are a random sample of the population of Vanderbilt
Engineering students. The results of this study will pose interesting problems that can be characterized
using confidence intervals and hypothesis testing. Once the data is collected, we will divide the class into
two subclasses; those who have a GPA greater than or equal to 3.0 and those who have a GPA lower
than 3.0. We will then find the average sleep length per night of each subclass. Whichever of these
subclasses has a greater number of data values will be used as our benchmark, and data taken from this
group will be accepted as the population average, to be used in later problem solving. We can then
conduct a hypothesis test with the null hypothesis being: X >= the average sleep length of the larger
pool (population average) and the alternate hypothesis with: X < the average sleep length of the larger
pool. We will examine the errors that go along with these hypotheses. The Type I Error: Assuming that
sleep length affects GPA, when in fact, it does not. Or Type II Error: Assuming that Sleep Length does not
affect GPA, when in fact, it does. From the combined pools of sleep length, we can also compute 90%,
95%, and 99% confidence intervals for the mean time a student spends sleeping and our margin of error
for each of them. Hopefully the results of this experiment will shed light on whether getting 8 hours of
sleep or just barely 6 or less, does or does not affect our grades.
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Authors:
Patrick M. Marine
Emily M. Ross
References:
1. The Relationship Between Sleep Length and Grade-point Average Among College Students:
College Student Journal: William Kelly, Kathryn Kelly, and Robert Clanton: 2001
2. Sleep Loss, Learning Capacity, and Academic Performance: Sleep Medicine Reviews: Giuseppe
Curcio, Michele Ferrara, Luigi de Gennaro: 2006