Coke or Pepsi?Coke or Pepsi?Alexandra V. GarrisonAlexandra V. Garrison

Austin M. LewisAustin M. LewisMath 005--ChanceMath 005--Chance

GoalsGoals

On campus, Coca-Cola On campus, Coca-Cola machines are in all of the dorms machines are in all of the dorms and sold in DDS establishments.and sold in DDS establishments.We want to determine whether We want to determine whether there is a difference between there is a difference between Coke and Pepsi.Coke and Pepsi.We more importantly want to see We more importantly want to see whether Dartmouth students whether Dartmouth students prefer Coke to Pepsi.prefer Coke to Pepsi.

Our Pre-Test ThoughtsOur Pre-Test Thoughts

We think that most students can tell the We think that most students can tell the difference between Coke and Pepsi.difference between Coke and Pepsi.We also believe that most students will prefer We also believe that most students will prefer Coke because it is so present on campus.Coke because it is so present on campus.Our prediction is that 80 percent of students will Our prediction is that 80 percent of students will prefer Coke.prefer Coke.We also believe that they will be able to We also believe that they will be able to determine which is Pepsi and which is Coke. determine which is Pepsi and which is Coke.

Other Thoughts….Other Thoughts….

We thought that it would be an We thought that it would be an overwhelming preference (80% or higher) overwhelming preference (80% or higher) because there are less options for Pepsi-because there are less options for Pepsi-drinkers.drinkers.

p=0.8 was our powerp=0.8 was our power

Coke or Pepsi?Coke or Pepsi?

The Actual TestThe Actual Test

We gave each subject a sample We gave each subject a sample of Coke and a sample of Pepsi of Coke and a sample of Pepsi without them knowing which one without them knowing which one is which.is which.We asked if they tasted a We asked if they tasted a difference.difference.If they detected a difference, we If they detected a difference, we asked which did they prefer.asked which did they prefer.Then we asked them to identify Then we asked them to identify which they thought was Coke.which they thought was Coke.

Null HypothesisNull Hypothesis

Our null hypothesis supports the idea that Our null hypothesis supports the idea that most of our subjects will be able to taste a most of our subjects will be able to taste a difference.difference.The subjects are like a fair coin; they are The subjects are like a fair coin; they are just as likely to pick Coke as they are likely just as likely to pick Coke as they are likely to pick Pepsi.to pick Pepsi.p=0.5p=0.5

Alternate HypothesisAlternate Hypothesis

Dartmouth students will prefer Coke over Dartmouth students will prefer Coke over Pepsi.Pepsi.

Because Coke is so readily available on Because Coke is so readily available on campus, our administration would invest in campus, our administration would invest in a company that students prefer.a company that students prefer.

p>0.5p>0.5

Our Binomial DistributionOur Binomial Distribution

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 5 9 13 17 21 25 29 33 37 41 45 49

Probability Under Null

Probability Under PowerHypothesis

DataDataData Chart A Year Gender Question #1 Question #2 Question #3

03, 04, 05, 06, 07 m, f yes, no right, left, other right, left, other#1 6 m yes left left#2 6 m no n/a n/a#3 7 f yes left right#4 7 m yes other left#5 7 m yes right right#6 7 f yes left left#7 7 f yes left right#8 5 f yes right left#9 5 m no n/a n/a#10 5 m yes right left#11 7 m no n/a n/a#12 7 f yes left other#13 6 m yes left right#14 7 f yes left right#15 7 m yes left right#16 7 f yes left left#17 7 f yes right left#18 6 f yes right right#19 5 m no n/a n/a#20 7 f yes right left#21 7 m no n/a n/a#22 7 m no n/a n/a#23 7 m yes right right#24 7 m no n/a n/a#25 6 m yes other left#26 4 f yes left left#27 6 m yes right right#28 6 f yes right left#29 4 f yes right right#30 7 f yes right left#31 7 f yes other right#32 5 m yes left right#33 4 f yes right right#34 6 f no n/a n/a#35 7 f yes right left#36 6 f yes left left#37 7 m yes right right#38 7 f yes left left#39 7 m yes right right#40 4 m yes left left#41 7 f yes left left#42 7 f yes left left#43 6 f no n/a n/a#44 4 m yes left left#45 4 m yes right right#46 4 f no n/a n/a#47 7 m yes right right#48 7 f yes left left#49 7 m yes left left#50 7 f yes left left

The Percentage BreakdownThe Percentage Breakdown

Coke=60%Coke=60%Pepsi=32.5%Pepsi=32.5%No preference=7.5%No preference=7.5%

Our ResultsOur Results

80% of the subjects were able to 80% of the subjects were able to distinguish the difference between Coke distinguish the difference between Coke and Pepsi.and Pepsi.Eighty-six percent of our subjects had a Eighty-six percent of our subjects had a preference…..preference…..But of those who did only 60% preferred But of those who did only 60% preferred Coke.Coke.This is significantly lower than our original This is significantly lower than our original belief of 80%.belief of 80%.

Actual Z-scoreActual Z-score

z-score = z-score = PPactutal – actutal – PPnullnull √√PPnullnull (1-(1- P Pnull)null)

NN0.60.6 – 0.5 – 0.5 √√(0.5)2 (0.5)2 = = 1.2651.265 4040

With a confidence level of 95%, our z-score With a confidence level of 95%, our z-score would have had to have been 1.65 to be able to would have had to have been 1.65 to be able to reject the null hypothesisreject the null hypothesis

Z-score of hypothesisZ-score of hypothesis

We calculated our original z- score to be -We calculated our original z- score to be -3.162.3.162.

With this score, the chance that 80% of With this score, the chance that 80% of students prefer Coke is 1/1000students prefer Coke is 1/1000

This shows that our test was not very This shows that our test was not very powerful so we should have had a smaller powerful so we should have had a smaller power hypothesispower hypothesis

Critical RegionCritical Region

Our critical region at the 5% level is Our critical region at the 5% level is P P ≥ ≥ 0.62020.6202

Unfortunately, our Unfortunately, our PP = 0.6 so we must = 0.6 so we must assume that more students chose Coke assume that more students chose Coke over Pepsi due to chance. over Pepsi due to chance.

Decision: Null or Alternate?Decision: Null or Alternate?

In the end, we found that we had to reject our In the end, we found that we had to reject our alternate hypothesis.alternate hypothesis.

A Type I error ocurredA Type I error ocurred

Our AnalysisOur Analysis

a Type I error occurred in which we had to a Type I error occurred in which we had to reject our alternate hypothesis and we reject our alternate hypothesis and we were forced to accept our null hypothesiswere forced to accept our null hypothesis

Because of our results, we cannot Because of our results, we cannot accurately assume that Dartmouth accurately assume that Dartmouth students prefer Coke, despite Coke’s students prefer Coke, despite Coke’s abundance on campusabundance on campus

Confounding FactorsConfounding Factors

Inadequate pallet cleansers, ie. Lays Inadequate pallet cleansers, ie. Lays Potato Chips, the salt hindered our Potato Chips, the salt hindered our subjects from tasting objectively.subjects from tasting objectively.It was not completely randomly selected. It was not completely randomly selected. Even though we asked many strangers to Even though we asked many strangers to participate in our test, there were quite a participate in our test, there were quite a few of our subjects who are friends.few of our subjects who are friends.