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3.2 Joint Probability
In the previous section, we began computing probability using some fairly basic ideas. In
calculating probabilities, we made a huge assumption: that the found number represents what
will occur in the long-run. For instance, if we conduct a study and find that out of 100 people, 94
respond positively to a new energy drink, can we conclude the drink is effective in providing
added energy
The answer to this question is
humbling: it depends upon how the
data was collected. Suppose the
participants are all college students
who tend to consume a large amount of
caffeine as it is. Would it be fair for the
advertisement to say, “There is a 94%
chance that this energy drink will
energize you” Not necessarily, since
the result only appeared to be valid in a
sample of college students. This means that the population must be specified form which the
sample was taken. In this case, the population is the set of all college students and the sample is
the 100 students who were selected. Thus, perhaps the advertisement should say, “Are you a
college student If so, there is a 94% chance that this energy drink will energize you” That is,
provided that this sample was a random sample and not a group of college students hand-picked
from the respective population.
Okay, so you have a data sample collected from a specific population and your goal is to now
talk about probabilities.
Example 1: Imagine that you work for a marketing agency and your goal is to determine the
effectiveness of two different branding approaches to a new line of clothing. The first approach
involves establishing a group of Facebook followers by giving incentives for discounts on
clothing by becoming a friend of the company. The company hypothesizes that seeing the
company logo under on their Facebook account each week,
they will gain a strong familiarity and comfort level with
the company‟s product. The second approach involves
hiring Hollywood actors to endorse the product at film
festivals and celebrity appearances. The company then
tracks the degree of success of the branding tactic by
measuring the number of retail outlets that agree to stock
the product based on the branding used. They find that, of
the 6 companies exposed to Tactic 1 (T1), 5 agreed to stock
the product. Of the 7 companies exposed to Tactic 2 (T2), 5
agreed to stock the product.
Statistics for Decision-Making in Business © Milos Podmanik Page 89