Coke or Pepsi?

1
Coke or Pepsi?

• Alexandra V. Garrison
• Austin M. Lewis
• Math 005--Chance

2
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.

3
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.

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Other Thoughts.

• We thought that it would be an overwhelming
  preference (80 or higher) because there are less
  options for Pepsi-drinkers.
• p0.8 was our power

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Coke or Pepsi?
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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.

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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.
• p0.5

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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.
• pgt0.5

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Our Binomial Distribution
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Data
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The Percentage Breakdown

• Coke60
• Pepsi32.5
• No preference7.5

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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.

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Actual Z-score

• z-score Pactutal Pnull
• vPnull (1- Pnull)
• N
• 0.6 0.5
• v(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

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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

15
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.

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Decision Null or Alternate?

• In the end, we found that we had to reject our
  alternate hypothesis.
• A Type I error ocurred

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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 Cokes abundance on campus

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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.