Stats Project 2007

Disclaimer

“This study was done = in an AP Statistics course with relatively small sample sizes. The validity of such studies must = always be questioned. Please keep this in mind if you use or report the results of this study.”

Abstract

Purpose: The purpose of this experiment is to see if there is a correlation between playin a professional footb= all game at “home” will increase winning percentage overall. We will check the home wins compared to the OVERALL wins, not just all games played= at home

There lie a few reasons for why teams may win more at home than they do away.

Travel Time: Teams do not have to = travel on a bus or plane to get to their playin field = and will be further rested

Home Field: Having a home field br= ings in fans and supporters to help cheer the team on, giving them a mental mora= le boost

Psychology: Teams believe that pla= ying at home (in tradition) will guarantee them a win.

Research Question: Will playing a professional football game at home yield a higher winning percentage?

Hypothesis: Playing a professional football game at home WILL y= ield a higher winning percentage.

Test: 1-proportion Z-test, α =3D .5

Methodology<= /o:p>

This research study was to determine whether or not playing a professional footb= all game at home will yield a higher winning percentage. In order to obtain a conclusion, we found the randomly selected five teams for the American Football Conference= and five teams from the National American Football Conference. For the five teams, we found their= total number of home win and their total number of wins overall. We found data from the 1996 season through the 2006 season.

After collecting the data, we found the average p(hat)= and ran a 1-proportion Z-test on a TI-83 calculator in order to determine if ho= me field advantage does result in higher winning percentages.

	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006
Oakland= Raiders	.571	.5	.5	.625	.583	.5	.545	1	.6	.5	1
San Die= go Chargers	.625	.5	.8	.5	1	.8	.625	.5	.583	.444	.571
Miami Dolphins	.5	.667	.7	.556	.455	.636	.778	.4	.75	.556	.667
Baltimo= re Ravens	1	.5	.667	.5	.5	.6	.571	.7	.667	1	.538
Denver<= /st1:City> Broncos	.615	.667	.571	.5	.545	.75	.556	.6	.6	.615	.444
St. Lou= is Rams	.667	.4	.5	.615	.5	.429	.857	.667	.75	.5	.5
Minnes= ota Vikings	.556	.556	.533	.6	.636	1	.667	.667	.625	.667	.5
Arizon= a Cardinals	.714	.75	.556	.667	1	.429	.6	1	.833	.6	.6
San Fra= ncisco 49ers	.5	.615	.667	.75	.667	.583	.5	.857	.5	.75	.571
New Yo= rk Giants	.5	.6	.625	.571	.417	.714	.5	.25	.5	.727	.375

Analysis<= /o:p>

Hypothesis: Ho: p =3D .5

&nbs= p; Ha: p > .5

Where p is the proportion of home wins over total wins.

Assumptions<= /o:p>

ü Sample is an SRS

ü Population is at least ten times the size of= the sample

ü np_o ≥ 10

n(1-p_o) ≥ 10

&nbs= p;

Z =3D (p(hat)-p_o) &= #8725; √(p_o(1-p_o)) ∕ n)

Z =3D (.62-.5) ∕ √(.5(.5)) ∕ 110)

Z =3D 2.5171 = p =3D .0059

Conclusion=

Since the = data gives us a p-value of p =3D .0059, the data is statistically significant at= the α<= /span>=3D.05 level. Therefore we can reject the null hypothesis that there is no home fi= eld advantage and that teams are equally likely to win away as they are at home= .

Our final = results may have a little bit of bias since we randomly picked teams. Some of the teams may have natural= ly been good every single year and possibly won most of their away games as we= ll.

However, w= e can assume that, generally, professional football teams are affected by home fi= eld advantage and generally have a higher winning percentage at home.

Resources<= /b>

www.pro-football-reference.= com

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By Chris Floyd and Josh Lau