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# The cola wars

## Discussion

1. Identify a member of your group who claims to be able to tell the difference between Pepsi and Coke. (Coke Classic, that is; accept no substitutes!) Design and carry out an experiment to test whether this is true. Remember that one swallow doth not a summer make: Don't certify your taste-tester just on the basis of one experiment. Decide exactly what data you will collect and what you will do with the data before you start collecting it. Also, remember the story of clever Hans, and consider the benefits of a double-blind study. (We also have RC cola available; if you prefer, you may want to see if your taste-tester can distinguish RC from Coke or Pepsi.)

2. Apparently, the formula for Coke was changed because taste tests showed that something like of Americans prefer the taste of ``new'' Coke to that of Coke Classic. Discuss the wisdom of this.

3. Why is there no such thing as Diet Coke Classic?

## Comments on the journals

• It is interesting to get people's opinions on probability paradoxes before and after an explanation. One student student asked four people with different educational backgrounds their opinion about the stick problem and reported that they all said 1/2 but three of the four agreed with 2/3 after an explanation. A school of psychology led by Stanford Psychologist Amos Tversky have studied how people answer probability problems and the effect or lack of effect of courses in probability and statistics on their answers. We will consider some of his work later.

• Referring to Nuclear reactor accidents the comment was made "You can't second guess human stupidity with numbers. Nor can you set numbers on something completely unexpected."

• A student would like to have some explanation of the doubling and splitting rules for blackjack that are claimed to be optimal. We will consider this also later. Watching the NCAA final four game, the same student comments "It seems that the so-called experts (sport casters) always try to support their theories and conclusions with stats. Unfortunately, there are always statistics that contradict the comments of the reporters.

• Most people felt that the ``reasonable doubt" should depend upon the nature of the crime. Indeed a recent news article claimed that it is understood in legal circles that beyond a reasonable doubt means a much higher probability in a criminal trial than it does in a civil suit. However, one student felt that ``Whatever crime or punishment is at stake, the theoretical amount of reasonable doubt should remain constant"

• Another student wrote about the attempts of the lawyers to appeal to the emotions of the jurors and the role that this might play the concept of ``reasonable doubt". She comments "I wonder if it is possible, or even likely, that numbers can be assigned to emotions. Love is an emotion. I have never once heard a friend say "Well, I'm 94.2%sure that I love Joe, but my reasonable doubt cutoff is 95%, so I guess I'll break up with him."

• A student gave in interesting analysis of an add by the TVTimes which stated the following:

Recently, Music Plus ran ads in TV Times and the regional edition of TV Guide, and measured response. Both ads featured an identical coupon off and ran at the same time. The results speak for themselves.

``TV Times was the clear winner. It generated almost four times as many responses as TV Guide. That translates into more traffic and more sales in our stores. I'm convinced TV Times is an excellent medium for reaching Southern California consumers."

## Assignments

### Journal

Read the current CHANCE news. Find an article that interests you and suggest some further questions that you would like to ask the persons involved in the research

### Homework due Thursday 29 April

Read Chapters 13, 14, and 15 of FPPA, and do the following review exercises: 1,2,6,8 of Chapter 13; 2,5,7 of Chapter 14 and 1,3,8 in Chapter 15.

Next: The binomial distribution Up: CHANCE Previous: The evil twin

snell@dartmouth.edu
Tue Jun 28 15:24:59 EDT 1994