Hats and Caps

1. Nick Joerger and Kevin Rogers Hats and Caps

2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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 mall

8. 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

9. 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 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. Ho: p=.5 Ha: p>.5 ^ p-p p(1-p) ^ x= 63 p=.6631 n=95 Z= n √ =3.1805

10. 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 distribution

11. College, Professional, Other, Company (con’t.) • 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 2 χ 2 2 =Σ = 12.006667 (obs-exp) (obs-exp) + … exp exp

12. Straight Brims • 2-prop Z test • In school vs mall • 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 xs= 25 ns = 47 xm= 19 nm = 48 Ho: ps= Ha: ps > pm pm ^ ^ Z= ps - pm =1.3299 • 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 √ ^ ^ p(1-p)(1/ 1/ nm ) ns + P( Z> 1.3299)= .091

13. 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.

14. 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

15. 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

16. 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.

17. 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