In this study we wanted to determine whether a later start
time affected the number of tardies at North Olmsted High School for
the first three quarters of the school year.
In order to test this hypothesis, we created a random sample
of 100 students by placing a complete student roster into Minitab
and doing a random sample.
After we had the sample we proceeded to look up schedules and
send out surveys anonymously to the students.
Our survey asked students to write both the number of
absences and tardies in the first three quarters of the 2013-2014
school year. Of the 100
sent out, we received 62 responses and used this data to calculate
both the mean and standard deviation of the tardies.
We obtained the mean number of tardies per student for the
first three quarters of the 2012-2013 school year from an
administrator. According
to guidance from our teacher, the standard deviation for 2012-2013
school year was estimated to be 5.
This was estimated based on an assumption that the data for
this school year would be positively skewed.
With this information, and the assumptions required to
perform a 2-sample t-test met, we were able to proceed with the
hypothesis test. We were
testing the hypothesis that µ1 =µ2 against the
alternative hypothesis that µ1 <µ2, with µ1
equaling the mean number of tardies per student in North Olmsted
High School during the first three quarters of the 2012-2013 school
year and with µ2 equaling the mean number of tardies per
student in North Olmsted High School during the first three quarters
of the 2013-2014 school year.
In this we were testing whether a earlier start time would
affect the number of tardies per student to increase or to remain the
same. From this test we
received a t-value of -2.147 at 61.586 degrees of freedom and a
p-value of 0.0179. Based
on a significance level of 0.05, we were able to reject our null
hypothesis and reach the conclusion that the mean number of tardies
after an early schedule is implemented increased from the previous
year.
Since this was an observational study, we were not able to
conclude causation to say that the earlier start time was the reason
for the increase in the number of tardies per student.
Since the two samples were from different years, both the
variables of weather and family issues may have varied causing a
different result. So,
the increase in tardies may not have been caused solely by the earlier
start time. This data
could be extrapolated to the entire North Olmsted population as well
as other high school populations with similar start time changes and
similar climate and social issues.
Specifically to the North Olmsted population, a study could
be conducted next year that is similar to the study conducted this
year. The start time for
next year is changing to be later so the number of tardies could be
tested again using data received from our test to see if a later
start time does decrease the number of tardies.