1. Hanover Tap Water Pre-Test
Math 5 Crew
Winter 2004

2. Goals:
To assess whether anecdotally observed ill feelings concerning the flavor of Hanover tap water are warranted.
More Precisely: We wish to establish whether there really is a substantial population of Hanover residents who actually prefer the taste of bottled spring water to local tap water (during winter).
More precisely, we wish to answer: “During winter, is any perceived preference a reality?”

3. My Pre-test Beliefs
Given samples of tap and bottled spring water, a substantial proportion of Hanover residents will prefer the bottled spring water.
More precisely, I felt that about 75% of residents will have a preference and…
of those who do, 80% or more will prefer the spring water.

4. Holy Cow! I was REALLY wrong!

5. Results
Indeed about 75% of my subjects had a preference (in my sample70%), but…
of those who did only 37.5% preferred the spring water!!!!
This means my 80% or higher belief only has a one in a hundred thousand chance of being true!

6. Whoa, Hold Your Horses!

7. Confounding Factors
This was not administered to a randomly selected set of residents, but rather to a Math 5 class that had thought carefully about this test beforehand.
The water was at room temperature and was brought to room temperature by leaving it in my office for two days and there were…

8. BUBBLES!

9. Well okay, these factors don’t seem all that confounding…
Conclusion: It seems that I am
very likely to simply be wrong.
Certainly my 80% belief
seems extremely implausible!

10. Now For Some Details… VS

11. The Test
Give a subject a sample of bottled spring water and a sample of Hanover tap water without telling them which is which.
Ask them whether they have a preference, and…
note their preference…

13. Null Hypothesis
The subjects that have a preference will be equally likely to prefer the tap water and the bottled spring water.
More precisely, let p be the percent of subjects that prefer the bottled spring water (among those that have a preference).
Null Hypothesis: p=0.5

14. The Alternate Hypothesis
Hanover residents will prefer spring water
In other words, p>0.5
Of course, what I really believed was…

15. What I believed
I felt that preference for spring water would be greater than or equal to 80%.
Hence, I used p=.8 to estimate the power of my test.
In other words, I used p=.8 to estimate how likely it is that if I am correct about what I believe, then my test confirms my belief.

17. Using a 3.2% Significance Level
The critical region for P is any percent greater than or equal to 70%

18. POWER
The power of my test is 81%

19. I Must Accept my Null Hypothesis!
I found P=37.5%

21. Interpretation
It looks possible that Hanover residents prefer tap water!!!!
There is a 15.3% chance of seeing a result this dramatic (in other words a percent this this low or lower) if the null hypothesis is true.
While not statistically significant, this result perhaps warrants a further study.

22. OOOOOPS!!!!!
Under the power hypothesis that p=.8 there is only a one in a hundred thousand chance that we see P=.375!
While there is a reasonable chance that there is no real preference, we have all but eliminated the possibility of a strong preference for bottled spring water.

23. Directions for future research
Test to see if we don’t “rest” the water, then we do see a preference for spring water?
Retest “rested” tap water to see if it really is preferred over Poland spring water.
Do both these experiments and then test the difference between these two percents. This will let us decide whether the resting process really improves the flavor of tap water.