Hanover Tap Water Pre-Test

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Hanover Tap Water Pre-Test

• Math 5 Crew
• Winter 2004

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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?

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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.

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Holy Cow! I was REALLY wrong!
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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!

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Whoa, Hold Your Horses!
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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

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BUBBLES!
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Well okay, these factors dont seem all that
confounding
Conclusion It seems that I am very likely to
simply be wrong. Certainly my 80 belief seems
extremely implausible!
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Now For Some Details
VS
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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

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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 p0.5

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The Alternate Hypothesis

• Hanover residents will prefer spring water
• In other words, pgt0.5
• Of course, what I really believed was

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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.

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Using a 3.2 Significance Level

• The critical region for P is any percent greater
  than or equal to 70

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POWER

• The power of my test is 81

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I Must Accept my Null Hypothesis!

• I found P37.5

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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.

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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.

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Directions for future research

• Test to see if we dont 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.