Confidence Interval MiniProject: Proportion of Players
Who Have Tattoos in the NBA
and NFL
Mr. Kiker 7th Period AP Stats
Drew Beathard
2-12-2015
Is
there a
higher
population proportion of players with tattoos on exposed body parts in the NBA or in the NFL?
That is the question that inspired my research for the Confidence Interval Mini-Project. I chose
to focus on this topic because of how it interests me personally. Not only do I love watching
sports, basketball and football included, but I love learning about particular player bios, who
they are, where they came from, and how they became successful in one of the most
competitive professions in the world. Thousands of people squeeze into stadiums to watch
sporting events, and millions more witness the action though their televisions. Many
professional athletes take advantage of these circumstances and express themselves through
tattoos. I want to find out which population, NBA or NFL, has a higher proportion of players
with tattoos that are exposed for people to see. This means tattoos on the head, neck, arms,
legs, or anywhere else that is exposed on live television. If either population does have a
significantly higher proportion, it could highlight a major factor that influences athletes to put
tattoos on their skin.
For this project, there were two populations: all current players in the National
Basketball Association (NBA), and all current players of 53 man rosters in the National Football
League (NFL). In the NBA, there are 443 players divided among 30 teams. In the NFL, there are
1696 players divided among 32 teams’ 53 man rosters. I conducted a slightly different sampling
procedure for the two populations. For NBA players, because the small population size, I was
able to find a list of all 443 players on one list. I then pasted this list to a document, with each
player labeled 1-443. Then, I used a Simple Random Sample of 40 players to research. For NFL
players, the population was much larger, and so I was unable to gather a list of all players in the
NFL. To dodge this obstacle, I designed a random block sample. First, I blocked the population
by the 32 teams in the NFL, each of which has a 53 man roster. Because each block was of equal
size, the method upheld an equal probability for each player to be selected. Next, I randomly
selected from the 32 team population 40 times. Finally, using each team’s 53 player roster, I
was able to randomly select one player from each of the 40 team selections, resulting in a
random selection of 40 players from the original population of 1696. Although this method was
the most random and accurate strategy for a random sample of NFL players, it may not have
been precisely representative of the entire population. This is because players are constantly
traded, dropped, and signed to and from teams, meaning that the list of players I gathered
(which was the most recent) may have changed since it was created. Regardless, I believe this
sampling method was sufficient in representing the population.
I calculated three different confidence levels for both the NBA sample and the NFL
sample. For the NBA sample, there was a sample proportion of 16/20, or .4. The confidence
intervals are as follows: 90% confidence= (.2726, .5274); 95% confidence= (.2482, .5518); 98%
confidence= (.2198, .5802). From these intervals, we can be 90% confident the true population
proportion falls between .2726 and .5274, 95% confident it falls between .2482 and .5518, and
98% confident it falls between .2198 and .5802. For the NFL sample, there was a sample
proportion of 24/40, or .6. The confidence intervals are as follows: 90% confidence= (.4726,
.7274); 95% confidence= (.4482, .7518); 98% confidence= (.4198, .7802). From these intervals,
we are 90% confident the true population proportion falls between .4726 and .7274, 95%
confident it falls between .4482 and .7518, and 98% confident it falls between .4198 and .7802.
These confidence intervals prove that it would be extremely unlikely for the population
proportion of the NFL to be lower than that of the NBA.
Through my research and data analysis during this project, I have been able to gather
statistics that strongly suggest that as a population, the NFL has a significantly higher
proportion of players with tattoos exposed on their bodies than the NBA. The 40 sample-size
proportion for the NFL was .6, which was much higher than the .4 proportion of the NBA. Now
that the big question has been answered, some other smaller questions arise. Why do NFL
players have, on average, more tattoos than NBA players? I have several hypotheses: it could
be because NBA players are much more exposed throughout their upper body and neck during
games, so they are influenced not to have tattoos. It could also be due to the large number of
foreign players in the NBA. While those questions remain unanswered, there is conclusive
evidence to suggest that, on average, a higher proportion of NFL players have tattoos exposed
on their bodies.
Handwork
Works Cited
NFL.com. NFL Productions LLC, 13 Feb. 2015. Web. 11 Feb. 2015.
"Player Index." NBA.com/Stats. 2014 NBA Media Ventures, 13 Feb. 2015. Web. 11 Feb. 2015.