Guess the Distance

1. Guess the Distance By Amanda Cunha and Ashley Kershaw

2. Description of topic • Depth perception- the ability to judge how far away an object is as well as how far away objects are from each other • With glasses depth perception can be impaired • This is because everything is simulated to be at the same distance • It is also said contacts can affect ones depth perception as well

3. Background of topic • We decided to test and see if there was a significant difference in the depth perception of those who wear glasses, contacts or neither • We also wanted to test and see if there was a difference in the depth perception of females vs. males

4. Procedure • We put one cone next to us at Macy’s at the Montgomery Mall • We measured 30 feet from the first cone and put a second cone there • We stood next to the door of Macy’s and as people entered or exited recorded… • Gender • Glasses- if we could see that • If no glasses were visible asked if they wore contacts • If they did not wear contacts, we recorded neither glasses nor contacts • We asked them to stand at the first cone and guess how far away the second cone was and recorded their answer • We went to Macy’s on Monday morning, Thursday afternoon, & Sunday evening

5. Exploratory Data: Contacts • The data is bimodal and slightly right skewed • The median is at 34ft and the IQR is 15ft • The range is 15ft to 60ft • There is a gap at 22ft and 55ft

6. Exploratory Data: Neither Contacts Nor Glasses • The data is unimodal and right skewed • The median is 34ft and the IQR is 17ft • The range is 15ft to 59ft

7. Exploratory Data: glasses • The data is unimodal with a right skew • The median is 35ft and the IQR is 20ft • The range is 15ft and 59 ft

8. Sample Population Females vs. Males at the Montgomery mall Population of people with contacts, glasses, or neither in Montgomery County

9. Conclusions Population In Montgomery County there is a greater population of people that wear neither glasses nor contacts. We then found that there is a greater number of people with contacts rather than glasses. The glasses population is the minority in Montgomery County. We found that there are more females going to the mall than males, which was expected.

10. 2 Sample T-Test • Ho: c/g = n • Ha: c/g n

11. Assumptions State Check • Two independent SRS • Popg/c 10ng/cPopn 10nn • Two normal populations or ng/c and nv 30 • They were not SRS but was the best sample and both were independent • There are more than 1130 people with glasses/contacts and 720 people with neither in Montgomery County • Ng/c (113) > 30Nv (72) > 30 Conditions Met – Student t-distribution -2 sample t-test

12. Calculations and Conclusions • Ho: c/g = v • Ha: c/g v = 1.317 2 P(t>1.317 df=154.2590) = 0.19 -We fail to reject Ho because the p-value of 0.19 is greater than alpha 0.05. -We have sufficient evidence that the average distance guessed by those with glasses or contacts is equal to the average distance guessed by those without glasses or contacts.

13. 2 Sample T-Test • Ho: c = g • Ha: c g

14. Assumptions State Check • Two independent SRS • Popc 10ncPopg 10ng • Two normal populations or nc and ng 30 • They were not SRS but was the best sample and both were independent • There are more than 500 people with glasses and 630 people with contacts in Montgomery County. • Nc (63) > 30Ng (50) > 30 Conditions Met – Student t-distribution -2 sample t-test

15. Calculations and Conclusions • Ho: c = g • Ha: c g = 0.303 2 P(t>0.303 df=105.931) = 0.76 -We fail to reject Ho because the p-value of 0.76 is greater than alpha 0.05. -We have sufficient evidence that the average distance guessed by those with contacts is equal to the average distance guessed by those without glasses.

16. 2 Sample t-Test • Ho: m = f • Ha: mf

17. Assumptions State Check • Two independent SRS • Popm 10nfPopm 10nf • Two normal populations or nm and nf 30 • They were not SRS but was the best sample and both were independent • There are more than 110 females and 750 males inMontgomery County . • Nf (110) > 30Nm (75) > 30 Conditions Met – Student t-distribution -2 sample t-test

18. Calculations and Conclusions • Ho: m = f • Ha: m f = -0.376 2 P(t<-0.376 df=81.7625) = 0.71 -We fail to reject Ho because the p-value of 0.71 is greater than alpha 0.05. -We have sufficient evidence that the average distance guessed by males is equal to the average distance guessed by females.

19. Application to Population • We conclude that regardless of wearing contacts, glasses, or neither the people of Montgomery County do not show a significant difference in depth perception. • We can also conclude that there is not a difference in the depth perception of males and females in Montgomery County.

20. Bias/ Error We found that people in groups guessed similar to each other, so they may not have been saying the distance that they actually felt. Some people did not take us seriously and said a random number when we asked for the distance between the cones. Since it was right after the holiday season, many people were in a rush and did not want to answer our questions. We faced the problem of involuntary response because not everyone wanted to answer our questions.

21. Personal opinions/conclusions • Our original hypothesis that there would be no difference in the depth perception of those with glasses, contacts, or neither was correct. • We felt that it was difficult to ask people to participate in our data collection when they were going in and out of the store. • Overall it was interesting to see the wide variety of response.