A Study Comparing Two Proportions - 2005-6
You have been accepted to college and also received the highest grade on the AP
Statistics examination given in May. Unfortunately, to skip the required freshman
statistics course, the Dean of your new school has asked you to submit an actual study
that demonstrates your knowledge of applied statistics.
PROJECT OVERVIEW
You must GATHER your own data that will allow you to do inferences using
Comparison of Proportions as described in Workshop Statistics Topic 24. You must
create a study that is not so obviously significant before the study that the study would be
meaningless. While you should/could suggest which one-sided hypothesis you hope to
confirm, the report must do a two-sided test to allow for the discussion of duality. If you
wish to follow up with a one-side test, feel free to do so.
EXPERIMENTAL DESIGN
• You must collect RAW data in order to answer a question which you create for a
sample you define with hopes of extending your conclusion to a population which you
determine. No surveys are allowed. Data may not be collected at BB&N.
• While the data must be collected in a way which fulfills the requirements of the test,
obtain the largest samples you can.
• If data is collected from human subjects, privacy must be maintained at all times. In
fact, in some circumstances, the release of personal data could be considered a violation
of school rules.
• If data is collected about human subjects without their knowledge, you must clear your
procedures with your teacher.
FORMAT AND STYLE
The report must have the following attributes:

 It must be word-processed using MS Word. If this is a hardship, speak to your
teacher immediately.

 No hand written material may be included except for the raw data. For example,
graphs & their scales, equations, and all symbols must be part of the computer file.

 A table of contents with correct page numbering. A table of contents can be
instantly generated by Word if you use the built in header styles of MS Word.

 A cover page. Stapled. NOT in a binder of any kind.

 Follow the AP guidelines on defining symbols that state:
Defining Symbols: Students should define all symbols when writing
solutions to open-ended questions. For example, when writing a null
hypothesis, a student should not write just  = 75, but should define what
represents. A clear and complete statement of a null hypothesis would
be: =75, where  is the mean of the reading test scores for all students in
the school.

 Use descriptive subscripts such as male rather than 1.
THE REPORT
The report should have each of the following sections (with appropriate subtitles) in the
order given:
A. The Abstract
A one page (not one word longer) overview of the study covering all the important
details. This page will have to impress the Dean. She will not even look at the rest of the
report unless she is impressed with the clarity, professionalism, and completeness of the
abstract in covering the crucial points of the study from beginning to conclusion. Here are
some hints learned from previous years:
• Do not write in the first person. Write in a scientific tone.
• State the research question in the opening. State what your goals were for this study.
What point did you wish to prove? Why did you expect that outcome?
• Discuss the population you considered.
• Mention the test you performed.
• Do not include any symbols except for p and n (as in p = ).
• Include brief suggestions for improvement and future research.
B. The Study
1. The Question: A description in every day English of the question you are trying to
answer.
2 Sampling: A careful description of how you obtained the samples. Be very specific.
Include sample sizes. The sampling process should be able to be replicated exactly
from your description. One or more meaningful digital pictures should be included
with appropriate captions. Note that these can make your file too big to email. Plan
ahead. They can be in a separate file referenced from this section. Digital cameras
may be borrowed from Mr. Coons.
3. Data: A summary of the data. You can include a copy of the data here but it is not
required since it involves entering it into the word processor. If you are good with
technology you can get it from your calculator to the word processor using the Graph
Link, but this is not required and not a good use of most student’s time. The actual,
hand written data as recorded in the field on the original paper must be in an appendix
submitted with the printed copy of this report and referenced here.
4. Significance Test: Complete all our expected steps of a test of significance. Make
sure the statistics are clearly stated before any calculations. This includes calculating
the test statistic without using the STAT/TESTS features of your calculator and
drawing a fully annotated diagram.
5. Compute and discuss the magnitude of your results without using the STAT/TESTS
features of your calculator
6. Convey your understanding of duality.
C. Discussion
1. Describe any weaknesses of your study. Describe any possible confounding. Where
possible, propose solutions to each problem given enough time and resources.
2 Extrapolate. What population do you feel comfortable extrapolating your results to?
Why?
3. Impress the Dean: In this section you are trying to show the dean that you understand
the other major idea presented in Topic 24 of Workshop Statistics (See page 514).
D. Conclusion

 The conclusion is most likely 3 or 4 solid paragraphs that are very contextual. It
should be clear what you studied, what you found out about your research question
and goal (while it is contextual you will mention sample sizes and p-value here).
However, there is little detail. It is an overview.

 Major weaknesses and ways to solve these problems should be mentioned (again,
no detail) along with your suggestions for future studies.
E. Optional Section: Power
•
Power of the Test: Once you have your results, do a detailed presentation (including
annotated graph) to determine an appropriate minimum sample size to have adequate
power to make this test worth performing.
•
This is a very open question and depends a great deal on your results. You will have
to meet with your teacher to discuss how you might approach this computation.
•
Only well organized, clear, complete presentations will be read. Up to 5 points of
optional credit is available. However partial credit will only be given for
substantially correct work.
WORKING WITH OTHERS
You may discuss any topic with other students. However, only you may collect the data,
do the calculations, and write the report.
CREDIT
This project is expected to be one of two or three projects this term, but it will be the only
significant project. For students completing the course in June, this project could be
worth as much as three-quarters of your project grade or perhaps as little as one-half. For
those seniors dropping the course for senior project, it will be the only project and worth
up to half you grade in March.
SUBMISSION
This project must be submitted in two ways. Late papers will have grade deductions:
  Electronically: Before the start of the class on the due date: as an attachment to an
email with the file name lastname_proj3.doc (example: coons_proj3.doc)
  Printed: Complete as you come into the classroom (rather than hoping to find a
stapler after you arrive).
-
end-
Examples:
Do you use your blinker?
A study comparing the proportion of males that use their blinker
when making the left turn onto Commercial street after crossing
the Charlestown Bridge versus the proportion of women that use
their blinker when making the left turn onto Commercial street
after crossing the Charlestown Bridge, in Boston, Massachusetts
Stefan Modzelewski
A Block AP Statistics
Graduation: 2006
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 research question for this study is: Does one gender tend to use their blinker
more than the other gender when making the left turn onto Commercial Street after
crossing the Charlestown Bridge in Boston, Massachusetts? The goal for this study
was to discover if there is a relationship between gender and the use of one’s blinker
at this turn. The conjecture that is being made is that men use their blinkers less when
making this turn. Men will use their blinkers less because they are more likely to
bend/break rules than women. Women on the other hand tend to be safer and do not
feel the need to test their boundaries and will use their blinker more often.
The population that was originally considered was all motor vehicles that make
the left turn onto Commercial Street after crossing the Charlestown Bridge. However,
this seemed much to broad so it was narrowed down to only motor vehicles that made
the turn between 3 and 5 o’clock in the afternoon on Thursdays, in clear weather (for
example no rain or snow). The study was performed on Thursday, February 23, 2006
between 3 and 5 o’clock.
The test that was used was a two proportion z-test. This test resulted in a p-value:
.3682. This is not statistically significant. Since the samples were two independently
selected samples there were two different values for n, for the males it was 50 and for
the females it was 33.
This study could be improved by taking a larger sample from multiple times and
days. That way a broader conjecture about a larger population could be made. Also it
would be interesting to see if the results differed if the person doing the study made
themselves as invisible as possible or if at all possible do the opposite and park a police
car at the corner of the intersection in a very visible place to where the cars are turning
and see if more people use their blinkers. It is also interesting to note that there seemed to
be a pack mentality with the use of the blinker or non use of the blinker. For example, if
the first car in line had their blinker on as they waited for the light to turn green, it
seemed like the cars behind it tended to also turn on their blinker. And vice versa if the
first car did not have its blinker on, it seemed that the car behind it was less likely to have
their blinker on and so on. This would make an interesting topic for a follow up study.
A Comparison of the Proportion of Men who buy Popcorn vs. the Proportion of Women
in the Movie Theater
Ben Brewer-senior ‘06
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.
The Abstract
The question that one is trying to answer is whether men proportionately
purchase more popcorn, when they go to the movie theater, then women do. The goals
for this study were to better understand who was buying popcorn. As a researcher, one
was hoping to find some trend or pattern which could shed some light on which gender
typically buys more popcorn. For this study, one is trying to find whether men buy more
popcorn then women, and as a researcher, one expects to see more men purchasing
popcorn then women because women tend to be more cautious about buying food in front
of others and stereotypically are more health conscious.
During this study, the population that was examined was all people who go to the
Loews Feshpond Cinema in Cambridge, Massachusetts. A two proportion z test was
performed which produced a P-value of .0029 with a male sample size of n=69 and a
female sample size of n=77.
In the future there are a few things that one can do to both improve the experiment
and also do additional research and experimenting based on some of the findings in this
experiment. First the study can be enhanced by increasing the days which the sample is
taken to include Saturday. This would in many ways help the study as it would allow the
researcher to get a larger sample size, as well as have a sample that included more teens,
thus better representing the population. Also one might try to change how the sampling
sheet is setup so that when a person buys a movie ticket they get a dash, and if they then
buy popcorn they get another dash. This would increase the accuracy and speed of the
sampling process allowing the research to more easily take a sample and assess the
population. Though there are some improvements that could be made to how the study
was conducted as a whole, the data collected from this study prompts further research on
popcorn and its consumption. For instance, one might want to look at if the time effected
how many people bought popcorn or what gender bought popcorn by taking samples at
different points in the day. One could also expand the project and look at what gender
bought any type of commodity from the concession stand as oppose to just popcorn.
Another study that one could do would be to look at people’s age and see whether
younger people tend to buy more popcorn or if older people get more. Finally, one could
conduct a study on whether people who do buy food at the theater, prefer to buy popcorn
or some other food such as nachos or hot dogs, or whether women tend to by smaller
sized popcorn then men.
Battle of the Sexes:
A Study Comparing the Proportion of Ads in the Male Teen Magazine,
Maxim, to the Female Teen Magazine, Cosmopolitan
By Chip Malt
DISCLAIMER
This study was one 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 question that this study is trying to answer is whether the ratio of advertisements to
pages in the female oriented magazine, Cosmopolitan, is the same as the male version of
the magazine, Maxim. Denis Publishing Company owns both of these magazines so it
was interesting to analyze if the proportion of ads to pages differed between the two
magazines because of their difference in audience. The goal of this study was to
randomly take six magazines out of the last thirteen published for each magazine (Feb.
2003-Feb. 2004 issues) and find the proportion of pages displaying ads of half page or
more and comparing them to the total number of pages in those magazines. The total
number of pages of advertisement for the combined six magazines, divided by the total
number of pages of the six magazines yielded the final proportion of advertisements per
page for Maxim and Cosmopolitan. These sample magazines gave a sample proportion of
x-barmaxim= 418/1066 and x-barcosmo= 660/1452.
The population that was studied was every magazine issue from the year 2003 and the
first three months of the year 2004. This population could be cautiously extrapolated to
each magazine issue of 2002 through the upcoming issues of 2004, assuming nothing
significant changes over this year.
At the beginning of the study it was expected that the female magazine, Cosmopolitan,
would have a higher proportion of advertisements per issue. This outcome was expected
because stereotypically women are known to be more avid shoppers than men, so
advertisers would spend more of their budgets displaying their product in a women-based
magazine than a male-based magazine.
The test performed on the sample was a two-sided, two proportion, Z-Test. A test of
significance and a confidence interval was applied to the sample and the duality between
the two was discussed. From the test of significance with nMaxim = 1066 and ncosmo= 1452,
a p value was found at p = .0018, which was significant at the predetermined alpha level
of α = .05. A 95% confidence interval produced an interval of (-.1013, -.0235) when phat Maxim – p-hat Cosmo. The confidence interval and test of significance both gave strong
evidence to reject the Null Hypothesis that the proportion of ads in Maxim is equal to the
proportion of ads in Cosmopolitan.
There were some weaknesses to this study. For instance, one of the magazines that was
picked randomly to use for the sample turned out to have a 20-page wedding special. This
"special magazine" yielded the highest proportion of advertisement pages to total pages
out of any of the twelve magazines. Another weakness in this study was lack of sample
size. Although over a thousand pages were used to calculate the test statistics, these
thousand pages only came from six magazine issues. If there was more money that could
be invested into the study, a random sample of a larger period of magazines could have
been taken, and more than six magazines from this larger period could be chosen for the
study. This could also increase the population that the data could be extrapolated to as
well as solve the small sample size issue.
There are many follow up studies that could be done with this data. One could conduct a
study showing the different genre of advertisements in the two magazines. For instance,
one could see if there are more beer or sports advertisements in Maxim, while there may
be more hair product or hygiene product advertisements in Cosmopolitan. Also, a follow
up study could test the ratio of advertisement pages to total pages depending on the
month. This study would show if there is a raising and lowering of the proportion of
advertisements in these magazines around Christmastime or other holiday times.