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Topic: [ap-stat] Fun Binomial Example
Replies: 1   Last Post: Nov 14, 2011 12:26 PM

 Dr. Eugene D. Gallagher Posts: 132 Registered: 12/3/04
RE: [ap-stat] Fun Binomial Example
Posted: Nov 14, 2011 12:26 PM

The last 14 Super Bowl coin tosses have been won by an NFC team (p value
= 1/16384). AFC (or AFL) teams have only won 14 of 45 Superbowl coin
tosses (two-tailed p value 0.0161).

http://www.profootballhof.com/history/release.aspx?release_id=1386

From: Julie Jones Laskay [mailto:julie_jones@ymail.com]
Sent: Monday, November 14, 2011 10:24 AM
To: AP Statistics
Subject: [ap-stat] Fun Binomial Example

Hi everybody,

I just wanted to share with y'all a fun binomial example that
illustrates some interesting points.

At the beginning of NFL games, a coin is flipped to determine which team
will decide if they will receive the ball to start the 1st or 2nd half.
The number of coin flips that a team wins can be modeled with a binomial
distribution where p = 0.5 and n = number of games. It's pretty easy
for me to convince myself that the flips are independent.

I live in New Orleans, and of course, we love our 2009 World Champion
New Orleans Saints.

This year, the Saints have played in 10 regular season games, and they
have lost EVERY coin toss. The probability of that happening is (10 C
0)*(.5^0)(.5^10)= 1/1024 = .0009765625.

I think that this is a great example because it shows a couple points:
-Even if something is unlikely to happen, it doesn't preclude it from
happening.
-In statistics, we use data to make conclusions. If something has a
.0009765625 chance of happening, we would conclude that if it happens,
then something suspicious is going on. However, there is no allegation
that the NFL is trying to get the Saints to lose the coin toss. After
all, what point would it serve?

As a follow-up, the Saints had a second coin flip yesterday at the start
of the overtime period. They lost that coin flip too.

On a personal note, I have really enjoyed using this example because it
is a fun way to start Monday morning AP Statistics class. It has really
helped my students understand the binomial distribution and appreciate
its importance.

Have a great week,
Julie

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