I found this pearl in Naked Statistics (chapter 5):
In 1981, the Joseph Schlitz Brewing Company spent $1.7 million for what appeared to be a shockingly bold and risky marketing campaign for its flagging brand, Schlitz. At halftime of the Super Bowl, in front of 100 million people around the world, the company broadcast a live taste test pitting Schlitz Beer against a key competitor, Michelob. Bolder yet, the company did not pick random beer drinkers to evaluate the two beers; it picked 100 Michelob drinkers.
It turns out, Schlitz's marketing department was not a bunch of idiots. And here's why.
If you toss a coin twice you can get either one of the following:
- heads, heads
- tails, tails
- heads, tails
- tails, heads
Therefore, the probability of getting one tails out of two flips is 2/4 (ie, case 3. and 4.).
That is described by the Binomial Distribution where n is the number of trials (coins) and k is the number of successes (tails):
p = n! / [k! * (n - k)!] * (1/2)^n
2! / [1! * (2 - 1)!] * (1/2)^2
2 / 1 * 1/4
1/2 (same as 2/4 from above)
The statisticians at Schlitz considered that:
- commercial beers taste the same
- in a blind tasting, a Michelob drinker would say that Schlitz tastes better 50% of the times (it's a coin flip)
- getting 40% or more of Michelob drinkers to say Schlitz is better is worth $1.7 million
But what's the probability?
If you take 10 Michelob drinkers, you need at least 4 successes. In other words, you want to sum the probability of 4, 5, 6, 7, 8, 9, and 10 tails with coin flips:
p = 10! / [4! * (10 - 4)!] * (1/2)^10 +
10! / [5! * (10 - 5)!] * (1/2)^10 +
...
10! / [10! * (10 - 10)!] * (1/2)^10
= 0,82
So there's a 82% chance of succeeding.
And if you raise the number of drinkers to 100, you get to a shocking 98%!