Red, White and What?
By Evan Widloski, Blake Griffith, Matt Howard and
Brittany Stinnett
Group Members
Evan Widloski– A lot sampler, tech support, and graphic
designs
Blake Griffith– C lot sampler and hypothesis tester
Matthew Howard– C lot sampler and graphic designs
Brittany Stinnet– B lot sampler
Data Collection
A recent news broadcast claimed that only 40% of
cars in America are actually American made. Our
group wanted to verify the truth in this claim by
examining the proportion of American cars that MHS
students drive to school every day. In order to do this,
we used the proportion of American cars in a small
sample to estimate the total number of American cars
at MHS.
Data Collection
In order to aid sampling, Evan used the Python programming language
to generate pseudo-random parking spaces numbered 001 to 391. Since
sampling each spot individually would require walking between parking lots
many times, the program sorts parking spots into their corresponding lots and
arranges them in consecutive order.
Data Collection
Our group met during 4th block to take to take a pilot study to ensure that our
sample would meet the conditions of normality. It is worth noting many
seniors leave school 4th block for dual enrollment classes, another potential
source of bias that cannot be easily accounted for. We split up the selected
spaces evenly and began sampling. If a spot was empty, the first occupied
space to the right was sampled instead. From this sample, we determined p̂
and q̂ to be 43% and 57% respectively which means that a sample of 100
spaces will meet the normality conditions.
Our actual sample was taken with the same
random sampling program. We simply took an SRS of
the 100 from the 391 spots and 15 minutes later our
data was recorded and placed into a spread sheet
Summary Statistics
Pilot Study:
p̂=.43
q̂= .57
Summary Statistics
Sample:
p̂=.41
q̂= .59
Summary Stats
As you can see, our pilot study, sample, and
hypothesis were all very similar and close.
Confidence Interval
State: We want to find a confidence interval
for the proportion of Maryville High School
drivers with parking spots in the three
official Maryville High School parking lots
that are American made with a 95%
confidence level.
Confidence Interval
Plan:
We should use a one-sample z interval for p if the conditions are satisfied.
We must check the 3 conditions:
Random: This condition is met because the parking spots were numbered from 000390 and randomly selected using a random number generator.
Independent: This condition is not met because there are not more than
100(10)=1,000 parking spots at Maryville High School, so we must apply the Finite
Population Correction Factor (sqrt((N-n)/(N-1))) in order to proceed in the testing.
Normal: This condition is met because:
np̂=(100)(.41)=41≥10
And n(1-p̂)=(100)(.59)=59≥10
Confidence Interval
Do:
A 95% confidence interval for p is given by
p̂±z*(sqrt((p̂(1- p̂)/n)))(sqrt((N-n)/(N-1)))
.41±1.96(sqrt((.41(.59)/100)))(sqrt((391-100)/(391-1)))
.41±1.96(.049183)(.863802)
.41±.083269
(.326731, .493269)
Confidence Interval
Conclude: We are 95% confidence from
.326731 to .493269 captures the true
proportion of American made cars driven by
Maryville High School students with a spot
in one of the three Maryville High School
parking lots.
Hypothesis Test
State: We want to perform a test at the
α=0.05 significance level of
Ho: p=.40
Ha: p≠.40
Where p is the actual proportion of cars
driven by Maryville High School students
with parking passes for a Maryville High
School lot.
Hypothesis Test
Plan: If conditions are met, we should do a one-sample z test for the population
proportion p.
We must check the 3 conditions:
Random: This condition is met because the parking spots were numbered from
000-390 and randomly selected using a random number generator.
Independent: This condition is not met because there are not more than
100(10)=1,000 parking spots at Maryville High School, so we must apply the
Finite Population Correction Factor (sqrt((N-n)/(N-1))) in order to proceed in
the testing.
Normal: This condition is met because:
npo=(100)(.40)=40≥10 Andn(1-po)=(100)(.60)=60≥10
Hypothesis Test
Do: The sample proportion of American-made cars in the Maryville High School
student parking lots is p̂=0.41
Test statistic: z=( p̂-po)/((sqrt(po(1- po)/n)*(sqrt((N-n)/(N-1))
z=(.41-.40)/((sqrt(.40(1- .40)/100)*(sqrt((391-100)/(391-1))
z=.01/((.048990)*(.863801))
z=.2363
Because this z-score does not fall into our rejection regions (z≤-1.96 or z≥1.96)
we fail to reject the null hypothesis.
Hypothesis Test
Conclude: Since our z-score of .2363 does
not fall into our rejection regions at z≤-1.96
or z≥1.96, we do not have sufficient
evidence to reject Ho. We cannot conclude
that the proportion of student-driven
vehicles that are parked in one of the official
school lots that are American-made differs
from the hypothesis of .40.
Conclusion
From our experiment we can conclude that the true proportion of
American made cars that are parked at our school is
approximately .4. We are surprised at how close to the news
broadcast that the proportion at Maryville High School actually
was. There were very few sources of possible error since
parking spots at Maryville High School are assigned to each
student. The most possible source of error is that a car was
parked in the wrong spot or that a student did not attend school
that day. We did not experience this issue however and our
experiment was a success.
Future Ideas
Future experiments could include taking samples of much
larger areas or by randomly selecting driveways in Maryville. An
area that we did not observe, but could be very interesting would
be to find the proportion of each make and see how this
compares to national and local sales of each brand of car.
Other experiments could also be based off of this study such as
grades as compared to car makes. Another interesting
experiment would be to find the correlation between first cars
and future income.
Raw Data