Disclaimer
This study was done in an AP Statistics
course with relatively small sample sizes. The validity of such studies must
always be questioned. Please keep this in mind if you use or report the results
of this study.
Abstract
The purpose of this study was to
determine approximately how long Tates Creek High School students spend in the
hallways with the hall pass. This study was performed in an effort to prove
that students remain in the hallway longer than teachers recommend, which is
approximately two minutes. This outcome was expected because it has been
observed through personal experience that students typically stay in the
hallways longer than two minutes. The sampled population was Tates Creek High
School students. A t-test was performed on the sample mean.
Methodology
This study was designed to determine
if Tates Creek High School students stay out in the hallway longer than the
recommended time of two minutes. We wanted to test this question because we
have noticed that students tend to stay in the hallways longer than the teachers
expect them to.
We started by numbering each
classroom in Tates Creek that had a class during the B-3 block and used a
random number generator to choose an SRS of 12 classrooms. We divided them up
so that each of the researchers would spend 100 minutes watching 4 classrooms,
or 25 minutes at each classroom. During this time, each researcher recorded how
long each student who left the designated classroom spent in the hallway. The
researchers sat in the hallway on the floor a short distance away from the specified
door. After this round of observations, we only had 21 data points, so we
decided to take another SRS of 6 classrooms. We repeated the same process, but
this time during the A-1 block, and ended up with a total of 34 data points. We
then performed a t-test on the mean time spent in the hallway.
Data Table
|
Room |
Time (min.) |
Room |
Time (min.) |
Room |
Time (min.) |
Room |
Time (min.) |
Room |
Time (min.) |
|
211 |
4.0833 |
709 |
5.75 |
808 |
9.5167 |
608 |
2.1667 |
308 |
2.95 |
|
309 |
5.2 |
709 |
2.65 |
808 |
9.1833 |
807 |
2.4 |
308 |
2.7167 |
|
706 |
0.3333 |
709 |
5.3833 |
313 |
4.3833 |
807 |
1.7333 |
308 |
2.6333 |
|
706 |
3.25 |
711 |
3.05 |
313 |
4.5167 |
513 |
2.8667 |
711 |
1.9167 |
|
706 |
1.7667 |
619 |
3.8833 |
313 |
2.1833 |
513 |
4.9833 |
711 |
2.7167 |
|
706 |
2.4333 |
619 |
2.5667 |
313 |
1.0333 |
513 |
2.7333 |
711 |
2.1833 |
|
706 |
3.8333 |
619 |
4.1667 |
313 |
1.7833 |
700 |
7.0167 |
|
|
Analysis
and Inference
Assumptions:
1.
The sample is an SRS
2.
The observations from the population
have a normal distribution
15 < n < 40
t is robust
proceed with caution
μ = mean number of minutes spent in the
hallways by students with hall passes
Ho: μ = 2 minutes
Ha: μ > 2 minutes
t* = 1.6924 (df = 33)
t
4.3580
α = .05
p = P( t > 1.6924 ) ≈ .00006
Since
our data yields a p-value of .00006, our data is statistically significant at
the α = .05 level. This means we can reject the claim that, on average,
students keep the hall pass out for two minutes for the claim that, on average,
students keep the hall pass out for greater than two minutes.
Possible
weaknesses and confounding that could have occurred includes classrooms where
no one came out, a small sample size, and somewhat short amounts of time to
watch each room. With the lack of time,
it was impossible to get abundant amounts of data, but with what we did get, we
can conclude that students do stay out of class for longer than the teacher-recommended
two minutes.