Hats and Caps

Nick Joerger and Kevin Rogers

Hats Research

We wanted to see and study how people wear hats, which style they wore their hat in (frontwards or backwards), the team or company the hat represents, and if the brim of the hat is bent or left straight

Using this we wanted to compare if hats in schools are different styles than what is commonly seen in public

Overall we wanted to see what style is most popular

Data Collection Procedure

All hats in school seen on the day we record data will be recorded and then on the weekend we will go to the mall and record every 3rd person we see with a hat. The categories we will use: if the person has the hat on frontwards or backwards. Also what team or company the hat represents, and whether the brim of the hat is straight or bent.

History of the Hat

The hat dates back to ancient Greece and Rome when hats were given to slaves who earned their freedom

Worn for religious reasons, covering from weather, safety, and as a fashion accessory

History of the Hat

1860 the modern rounded baseball cap was created

Colorado 1865, the 10 gallon hat was created

1900 the Brooklyn style cap became popular

The bill or brim was designed to protect player's eyes from the sun

Front vs Back

The number of people wearing hats backwards is greater in school than in the mall

Overall about 2/3rds of people wear their hat frontwards frontwards

66%

34%

Total

back-wards

Frontwards62%

38%

School

backwards

frontwards71%

backwards29%

Mall

Team/Company/Other

In both locations the number of professional hats was much greater than all other categories

Fewer college hats were found in the mall

college professional other company

9

24

4

13

3

28

9 10

Hat Categories

Series1 Series2School

college

12

52

1323

Total

professionalother company

mall

Bent vs Straight Brim

In school the ratio was almost even

In the mall there was 10 more people with bent brims then straight brims

bent brim straight brim

2919

22

25

Bent Brim vs Straight Brim

Mall School

Frontwards

1 prop Z test Proportion of frontwards hats over hats with brims

State • n*p≥10 •n*(1-p)≥10 •SRS •Large pop. ≥10*n

Check• 95*.5≥10 •95*(1-.5)≥10 •SRS •Large pop. ≥10*95

√Z=

p-p^

p(1-p)n

=3.1805

Ho: p=.5 Ha: p>.5

x= 63 p=.6631 n=95

^

P(Z≥3.1805)=7.351*10^-4

• We reject Ho because the p-value<α=.05 •We have sufficient evidence that the true proportion of people who wear their hat, assuming it has a brim, frontwards is greater than .5.

College, Professional, Other, Company

Chi squared goodness of fit test

Ho: The observed frequency distribution of types of hats fits the expected distribution Ha: The observed frequency distribution of types of hats does not fit the expected distributionObserved Expected

College 12 25

Professional 52 50

Other 13 10

Company 23 15

College, Professional, Other, Company (con’t.)

χ2= Σ

(obs-exp)

2

exp

(obs-exp)

2

exp+ … =

12.006667

State •SRS •Large n so that all expected counts ≥ 5

Check •Assumed •Assumed

P(Χ2 > 12.00667 l df=3)=.00736

•We reject Ho because p-value< α=.05 •We have sufficient evidence that the observed frequency distribution of types of hats does not fit the expected distribution

Straight Brims

2-prop Z test In school vs mall

Ho: ps

=

pm

Ha: ps >

pm

State •2 indep. SRS• n*p ≥10•n(1-p) ≥10 •n*p ≥10•n(1-p) ≥10 •Pop. School ≥10*n •Pop Mall ≥10*n

Check•assumed• 47*.53 ≥10•47(1-.47) ≥10 •48*.4 ≥10•48(1-.6) ≥10 •Pop. School ≥10*47 •Pop Mall ≥10*48

Z=

ps -

pm̂^

√p(1-p)(1/ns

+

1/ nm )^ ^

=1.3299

xs = 25

ns = 47

xm = 19

nm = 48

P( Z> 1.3299)= .091

•We fail to reject H0 because p-value> α =.05 •We have sufficient evidence that the proportion of hats with brims being straight in school is equal to the proportion in the mall

Conclusion

In our first test, we found that the proportion of hats that have brims that are worn frontwards is greater than .5, meaning that more people wear their hats frontwards. In our second test we found that the most common type of hat to be worn is a professional sports team, followed by company hats, and then college and other being about equal, both in school and the mall, which did not fit the expected distribution. In our third test we found that the proportion of hats being worn that have brims that are straight is not significantly different than in the mall.

We have found that most hats worn have brims. We have found that the number of hats with straight brims in school is not significantly different that hats with straight brims worn in the mall. We have also noticed in school that straight brims are more popular meanwhile in the mall bent brims appear to be more popular. Also both in school and the mall more frontwards hats to backwards hats seem to be worn; roughly having a proportion of 2:1, meaning that it is more popular to wear a hat frontwards.

Application to Population

Most hats have brims More hats are worn frontwards than

backwards Professional sports teams hats are

the most popular and then company hats

The least popular types of hats are college and other

The number of straight brims roughly equals the number of bent brims

Bias/Error

Only surveyed in school one day Only surveyed one school Mainly surveyed youth so didn’t get

the styles of older people Surveyed areas near professional

sports teams Only surveyed in the mall one day Only surveyed one public place

Personal Conclusions

We feel that this was an interesting project. I do not feel that our results were that in-accurate but I do think to improve it we could take samples from multiple schools and public places over many days. I feel if we did that we would get accurate results. But overall, I enjoyed this project and think we did a good job.

Sources of Data/Research

Central Bucks High School South Montgomery Mall of Montgomery

County, PA http://en.wikipedia.org/wiki/Baseball_

caps

http://www.hatsuk.com/hatsuk/hatsukhtml/bible/history.htm