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.

4. Other Thoughts…. • We thought that it would be an overwhelming preference (80% or higher) because there are less options for Pepsi-drinkers. • p=0.8 was our power

5. Coke or Pepsi?

6. 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.

7. 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

8. 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

9. Our Binomial Distribution

10. Data

11. The Percentage Breakdown Coke=60% Pepsi=32.5% No preference=7.5%

12. 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%.

13. 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

14. 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.

16. Decision: Null or Alternate? • In the end, we found that we had to reject our alternate hypothesis. • A Type I error ocurred

17. 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

18. 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.