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```AP STATISTICS
PROJECT #3
The Product Proportion Comparison Project
You have just been hired as marketing researchers within a particular company. Your
task is to prove or disprove the company’s current claim concerning their product by
comparing it to TWO other similar products through a survey or an experiment. Your
result will be written up in a report to the CEO along with all supporting data.
For example: PEPSI ‘s current position is that a higher proportion of the population drinks PEPSI
than COKE or Dr. Pepper. You would conduct an experiment/survey, collect the data, and compute
the sample proportions. You would then conduct a Significance Test to determine whether there
actually is a difference in proportions.
For example: CHIPS A’HOY, the chocolate chip cookie company, has a current position that there are a
higher proportion of chips in their cookies than NESTLE . You would carry out an experiment that would
examine the proportion of cookies that have an average amount of chips, calculate the proportions, and then
conduct a Significance Test to determine whether there actually is a difference in proportions.
For example: ATT advertises that there are a significantly different proportion of people using ATT than
MCI. You would conduct an experiment/survey, collect the data, and compute the sample proportions. You
would then conduct a Significance Test to determine whether there actually is a difference in proportions.
PART I - ONE – PROPORTION COMPARISON
1. Choose a particular company that sells, markets, and advertises a certain product or idea.
company’s product or idea that you are investigating.
2. DESIGN a Survey or an Experiment to examine and compare the company’s product or
idea with TWO other companies of similar products. You will survey or use an experiment
to determine which one of the three products/concepts the respondent prefers best. Your
sample must be (but not limited to) a sample size of 45. Describe how you carried out this
survey or experiment? How was randomization incorporated in your design? This
description should be very detailed. How did you avoid many of the cautions associated
with experimental design or sampling? Could there be any sampling bias? Are there any
confounding variables? How did you address them?
3. The experiment should establish three separate counts, the number of respondents that
respond favorable to each of the three products. a = the number of respondents in favor
of your product, b = the number of respondents in favor of your alternative product #1, and
c = the number of respondents in favor of your alternative product #2. Create a histogram
representing the percent of respondents in favor of each or three products.
Probability
4. Showing all work, calculate the probability that more than half of the respondents favored
5. Showing all work, calculate the probability that less than a third of the respondents favored
Confidence Intervals
6. Showing all steps of a Confidence interval, calculate the true proportion of the population
that favors your product. (Be sure to check the assumptions and answer in context.)
7. Showing all steps of a Confidence interval, calculate the true proportion of the population
that favors alternative product #1. (Be sure to check the assumptions and answer in
context.)
8. Showing all steps of a Confidence interval, calculate the true proportion of the population
that favors alternative product #2. (Be sure to check the assumptions and answer in
context.)
Hypothesis Tests
9. It has been claim that more than 50% of the population favors your product. Use your
collected data and a one proportion hypothesis test to determine if there is any evident
disregarding the claim. State your Parameters, Hypothesis, Test Name AND Formula,
state the results in context, and test the assumptions.
10. Conduct a TWO separate Two-Proportion hypothesis tests to determine if YOUR product is
preferred more than the first or second alternative product. In the first hypothesis test use
the data collected for your product and the first alternative. In the second hypothesis
test use the data collected for your product and the second alternative.
For both tests, is there significant evidence that your product is more widely favored over
the alternative? State your Parameters, Hypothesis, Test Name AND Formula, state the
results, and test the assumptions.
THE REPORT
You must prepare a letter to the CEO of your company, which is ME (Mr. Lance A. Belin). In this
report, comment about favorability of your product. This report must be a 100% typed report with
at least 200 words, have a cover page, have a very creative title, be very detailed, include a
statement of what you expected before the experiment, how you collected the sample, and include
a description of the results. The report should include support for your conclusion with p-hats,
graphs, hypotheses, assumptions, z-scores, p-values, and conclusions in Laymen’s terms.
Finally, based on the results of all inferences, how should the company change their current