o We chose to do our project on cars in South's parking lot to see if our parking lot could be considered representative of the entire population of cars.

Descriptiono We chose to do our project on cars in

South's parking lotto see if our parking lot could be considered representative of the entire population of cars

o We studied many aspects of them like color, size, type, etc. to try and make conclusions about the population

o We went outside in the parking lot to explore!

History of Cars

o 1769- First self-propelled caro 1886- Internal combustion engines

developedo 1896- First road traffic deatho 1997- Green cars

Taking the Sample

o Every 5 cars in CB South parking lot

o More variables to decide from Color Type (Car, SUV, Truck, Other) Number of Doors

Sampling Results

Red SilverGreen Blue White Black Other Total

2-Door Car 3 3 1 0 4 2 1 144-Door Car 6 20 7 5 7 7 5 57

SUV 2 6 3 4 5 3 1 242-Door Truck 0 1 0 1 0 1 1 44-Door Truck 0 0 0 0 1 2 0 32-Door Other 1 0 0 0 0 0 1 24-Door Other 3 2 1 3 2 0 1 12

Total 15 32 12 13 19 15 10 116

Cars SUVs Trucks Other0

10

20

30

40

50

60

70

80

Type Of Vehicle

Type Of Vehicle

Nu

mb

er

Of

Veh

icle

s

Cars

SUVs

Truc

ks

Oth

er0

10

20

30

40

50

60

70

80

Type Of Ve-hicle

Type Of Vehicle

Nu

mb

er

Of

Veh

icle

soChose to this graph to

display the overall results in a simple and general form

oMajority of vehicles are cars

oFew trucks, but may be different in population where more workers use trucks to transport heavy items

0

5

10

15

20

25

30

35Total Color of Vehicles

OtherTrucksSUVsCars

Color Vehicle

Nu

mb

er

Of

Veh

icle

s

0

5

10

15

20

25

30

35 Other

Trucks

SUVs

Cars

Color Vehicle

Nu

mb

er

Of

Veh

icle

s

Colorso Used this graph because it’s more specific but not too specifico Shows silver is the main color of the populationo Most colors have about equal amounts of SUVs

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%Total Color of Vehicles

Other

Trucks

SUVs

Cars Color Vehicle

Nu

mb

er

Of

Veh

icle

s

Red Silver Green Blue White Black Other0

5

10

15

20

25

30

35

Color and Type4-Door Other2-Door Other4-Door Truck2-Door TruckSUV

Color Vehicle

Nu

mb

er

of

Ve-

hic

les

Red SilverGreen Blue White Black Other0

5

10

15

20

25

30

35

4-Door Other2-Door Other4-Door Truck2-Door TruckSUV4-Door Car2-Door Car

ColorN

um

be

r

Color and Type

o Stacked bar grapho Shows all variableso Silver 4- door cars are

dominanto Blue has no 2- door

cars, so in the population they must be minimal

Tests We Usedo Chi- Square Test: Goodness of

Fito Uniformo Our Sample vs. North America

o Chi- Square Test for Association: Color vs. Car Size

o One Proportion Z Test for SUVso One Proportion Z Interval for

SUVs

Assumptions for Goodness of Fit

o Assumed (we performed the test)

o √ (all expected counts are 16.5714)

o SRSo Sample size large enough that all expected counts are greater than or equal to 5

2

2 Goodness Of Fit

We found a website releasing the car colors of 2006 in North America from the DuPont Annual Color Popularity Report. We decided to see if this distribution (“overall”) fit the distribution of car colors from CB South’s parking lot. We included light brown and yellow/gold in the “other” category, making “other” 11%. We included silver and gray together, as we had in our study, making “silver” 32%. We also combined white pearl with white, making “white” 19%.

Test – Goodness of Fit

Expected: Red - (.11)(116) = 12.76Silver - (.32)(116) = 37.12Green - (.04)(116) = 4.64Blue - (.11)(116) = 12.76White – (.19)(116) = 22.04Black – (.13)(116) = 15.08Other – (.11)(116) = 12.76

Observed: Red - 15Silver - 32 Green - 12Blue - 13White - 19Black - 15Other - 10

Ho: The observed frequency distribution of car colors fits the expected.Ha: The observed frequency distribution of car colors does not fit the expected.

Check• Assumed• Does not check- Since green’s expected

count of 4.64 is close to 5 we proceed

State• SRS• Sample size large enough so all

expected counts ≥ 5

12.37

)12.3732(

76.12

)76.1215(

exp

)exp( 2222

ected

ectedobserved …= 13.7952

2

0320.)7952.13( 2 p

df=6α=.05

Test – Goodness of Fit2

We reject Ho in favor of Ha because p-value of .0320 < α =.05. We have sufficient evidence that the observed frequency distribution of

car colors does not fit the expected distribution. 

The category of green seemed to be the category furthest off. We suspected that if green were not part of the test, we might have failed to reject. Even though our p-value was still less than .05, it was much higher

than our p-value in the previous test, which was .0032. 

We could have improved this test by having a sample size large enough that all expected counts were greater than 5. Perhaps we could have included green in the “other” group in order to avoid this problem, or we could have increased

our sample size (every fourth car instead of every fifth, for example).

0320.)7952.13( 2 p

Ho: The observed frequency distribution of car colors fits the expected.Ha: The observed frequency distribution of car colors does not fit the expected.

2 Test of AssociationState• Two Independent SRS• Sample size large enough that all

expected counts ≥ 5

Check• Assumed• Does not check- we choose to proceed

Ho: Car color and size are independent.Ha: Car color and size are dependent.

Red Silver

Green

Blue White

Black Other

Small 9.181 19.586

7.345 7.957 11.629

9.181 6.1207

Large 5.819 12.414

4.655 5.043 7.371 5.819 3.879

586.19

)586.1923(

181.9

)181.99(

exp

)exp( 2222

ected

ectedobserved

5922.)629.4( 2 p

…=4.629

df=6 α=.05

2 Test of Association

We fail to reject Ho in favor of Ha because p-value of .5922>α=.05. We have sufficient evidence that car color and size are independent.  o Chose to this test to see whether or not there was an

association between the size of the car and its coloro Thought that it was more likely for a small, sporty car to be a

flashy color like red rather than a large truckoGrouped our sample into two categories: oSmall, for cars, and large, for SUVs, trucks, and otheroBecause the samples of SUVs, trucks, and other vehicles were

too small to be statistically viable on their own. ***We concluded that there was no association between car color and size. Thus, it is no more or less likely for a large car to be a certain color than a small car. ***

Red

Silv

er

Green

Blue

Whi

te

Black

Other

05

10152025

Size vs. Color

Small

Large

Color

Nu

mb

er

of

Cars

Comparing Size and Color

o Displays the amount of cars of each color

o Stacked bar graph helps us easily compare the car sizes to the color.

For the most part, the number of small cars of each color is greater than the number of large cars because our sample of small cars was so much greater. The exception is blue, where the number of large cars of that color is greater than the number of small cars.

One Proportion Z Test for SUVs

Ho: p=.3Ha: p<.3

State• SRS• np ≥10• n(1-p)

≥10• pop ≥

10n

Check• Assumed• 116×.3 ≥10• 116×.7 ≥10• pop ≥1,160

1882.2)1(

ˆ

npp

ppz

01433.)1882.2( zPWe reject Ho in favor of Ha because the p-value of .01433 is greater than α=.05. We have sufficient evidence that the proportion of SUVs is less than .30.

We decided to do this test because we felt that the proportion of SUVs was almost .5, so we used .3 because we knew the proportion wouldn’t be that close to .5. We felt that the proportion of SUVs would be less than .3 because they use a lot of gasoline and the majority of people are trying to become more eco-friendly.

One Proportion Z Interval for SUVs

Confidence level of 96%

State• SRS• np ≥10• n(1-p)

≥10• pop ≥

10n

Check• Assumed• 116×.3 ≥10• 116×.7 ≥10• pop ≥1,160

)19329,.06533(.)ˆ1(ˆ

*ˆ

n

ppzp

1293.ˆ p

We are 96% confident that the proportion of SUVs lies between .06533 and .19329.

We decided to do interval because we wanted to find out where the actual proportion of SUVs fell. By doing a confidence interval we found that the proportion of SUVs is not that high compared to what we originally thought. People really are becoming more eco-friendly!

Mistakes

o Not every car in the parking lot is there everyday, so we probably missed someo We did not meet all the assumptions, but we continued with the testsoWe should have picked the cars by using a software to randomize which cars we looked at by their spot number

Our Conclusionso Expected the main colors to be black and whiteo Large amount of red was surprisingo Silver is very popularo School parking lot doesn’t seem to match national

distribution of carso Could have improved chi- square test by increasing the

sample size so that all expected counts were greater than or equal to five.o Every 4 cars instead of 5o Stratified random sampling would have worked better

in this caseo Split the cars in the parking lot into small cars and

large cars and taken a simple random sample of the small cars and a simple random sample of large cars. Therefore, both samples would be sufficiently large enough for the assumptions to pass.

Our Opinions

o Too much work in too little time!o Way too cold and should have found a

different way to sampleo Liked looking at cool car pictureso Glad it’s over