Transcript Coke or Pepsi? - Dartmouth College

Coke or Pepsi?
Alexandra V. Garrison
Austin M. Lewis
Math 005--Chance
Goals
On campus, Coca-Cola
machines are in all of the dorms
and sold in DDS establishments.
We want to determine whether
there is a difference between
Coke and Pepsi.
We more importantly want to see
whether Dartmouth students
prefer Coke to Pepsi.
Our Pre-Test Thoughts
We think that most students can tell the
difference between Coke and Pepsi.
We also believe that most students will prefer
Coke because it is so present on campus.
Our prediction is that 80 percent of students will
prefer Coke.
We also believe that they will be able to
determine which is Pepsi and which is Coke.
Other Thoughts….
We thought that it would be an
overwhelming preference (80% or higher)
because there are less options for Pepsidrinkers.
p=0.8 was our power
Coke or Pepsi?
The Actual Test
We gave each subject a sample
of Coke and a sample of Pepsi
without them knowing which one
is which.
We asked if they tasted a
difference.
If they detected a difference, we
asked which did they prefer.
Then we asked them to identify
which they thought was Coke.
Null Hypothesis
Our null hypothesis supports the idea that
most of our subjects will be able to taste a
difference.
The subjects are like a fair coin; they are
just as likely to pick Coke as they are likely
to pick Pepsi.
p=0.5
Alternate Hypothesis
Dartmouth students will prefer Coke over
Pepsi.
Because Coke is so readily available on
campus, our administration would invest in
a company that students prefer.
p>0.5
Our Binomial Distribution
0.16
0.14
0.12
0.1
Probability Under Null
0.08
Probability Under Power
Hypothesis
0.06
0.04
0.02
0
1
5
9 13 17 21 25 29 33 37 41 45 49
Data
Data Chart A
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Year
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Gender
m, f
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Question #1 Question #2
yes, no
right, left, other
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Question #3
right, left, other
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The Percentage Breakdown
Coke=60%
Pepsi=32.5%
No preference=7.5%
Our Results
80% of the subjects were able to
distinguish the difference between Coke
and Pepsi.
Eighty-six percent of our subjects had a
preference…..
But of those who did only 60% preferred
Coke.
This is significantly lower than our original
belief of 80%.
Actual Z-score
z-score = Pactutal – Pnull
√Pnull (1- Pnull)
N
0.6 – 0.5
√(0.5)2
= 1.265
40
With a confidence level of 95%, our z-score
would have had to have been 1.65 to be able to
reject the null hypothesis
Z-score of hypothesis
We calculated our original z- score to be 3.162.
With this score, the chance that 80% of
students prefer Coke is 1/1000
This shows that our test was not very
powerful so we should have had a smaller
power hypothesis
Critical Region
Our critical region at the 5% level is P ≥
0.6202
Unfortunately, our P = 0.6 so we must
assume that more students chose Coke
over Pepsi due to chance.
Decision: Null or Alternate?
In the end, we found that we had to reject our
alternate hypothesis.
A Type I error ocurred
Our Analysis
a Type I error occurred in which we had to
reject our alternate hypothesis and we
were forced to accept our null hypothesis
Because of our results, we cannot
accurately assume that Dartmouth
students prefer Coke, despite Coke’s
abundance on campus
Confounding Factors
Inadequate pallet cleansers, ie. Lays
Potato Chips, the salt hindered our
subjects from tasting objectively.
It was not completely randomly selected.
Even though we asked many strangers to
participate in our test, there were quite a
few of our subjects who are friends.