Is There an Association Between Whether a Person Drives a Car or Truck/SUV and the Color of Their Vehicle?

Gina Ballard

AP Statistics

B-3

Disclaimer:

This study was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this study.

Abstract:

This observational study was done to answer the question of whether or not the type of vehicle a person owned had an effect on the color the owner chose. Most of the time a person thinks of a truck they picture a red one, or they think of a black SUV. When a person thinks of a car and they think of gray or white. When looking for a used car the person buying may find that it is hard to find certain colors. This is because there may be an association between the type of vehicle and the color of it.

The population tested was cars and trucks/suvs of Lexington, Kentucky. The sample size was 342 vehicles. After collecting the data, the next step is to perform a chi-squared test to find the results. The data will be tested at an alpha= .o5 level. That way if the p-value is anything less than .o5, then that would suggest that an association existed.

Methodology:

The question this study asks is whether or not there is an association between the type of vehicle, car or truck/suv, and the color of the vehicle. Basically this study was done to test whether or not there are certain popular colors for cars and different colors that are most common for trucks/suvs.

To answer this question, the first step is to start with an observational study. The random samples were taken from two Lexington parking lots. To randomize in this study two parking lots were randomly selected. Then the cars were viewed down the aisles. One of the parking lots was Fayette Mall and the other Wal-Mart. This way the sample would be form a parking lot that was mainly of upper-class/middle-class cars and the other of lower-class/middle-class. Since the mall contains many expensive department stores and Wal-Mart is a discount store. The colors the cars were classified as were: maroon, black, blue, tan, red, green, white, and gray. The cars for this study are a typical car, and either a truck or suv.

Once the data was collected it was analyzed through a chi-squared test. The expected counts were calculated as were the chi-squared components and ultimately the chi-squared value. The P-value was also found, which showed whether to reject or fail to reject Ho at an alpha = .05 level.

Graphs:

Chi-Square Test: cars, truck/suv

Ho: There is no association between the type of vehicle a person drives (car or truck/SUV) and the color they choose for their vehicle.

Ha: There is an association between the type of vehicle a person drives (car or truck/SUV) and the color they choose for their vehicle.

Assumptions:

ü None of the Expected values are less than one

ü No more than 20% of the expected values are five or less

*Expected counts are printed below observed counts

cars trucks/suvs Total

Black 30 15 45

32.37 12.63

Maroon 25 6 31

22.30 8.70

Gray 36 9 45

32.37 12.63

White 42 10 52

37.40 14.60

Blue 36 14 50

35.96 14.04

Tan 23 12 35

25.18 9.82

Red 22 20 42

30.21 11.79

Green 32 10 42

30.21 11.79

Total 246 96 342

Chi-Sq = 0.173 + 0.444 +

0.327 + 0.839 +

0.407 + 1.044 +

0.565 + 1.447 +

0.000 + 0.000 +

0.188 + 0.482 +

2.231 + 5.718 +

0.106 + 0.272 = 14.244

DF = 7, P-Value = 0.047

Conclusion:

Ho is rejected in favor of Ha at an alpha = .05 level since the p-value of .047 is just below .05. There is an association between whether a person drives a car or truck/SUV and the color of their car.

There may be some weakness in this study. The original study was going to test the relationship between the color of a car and type of car, with each category of vehicles. For this study the vehicles were classified as car, truck, SUV, van, and sports car. But the data failed the assumptions for the chi-square test. So the data was rearranged to fit the assumptions. Although the data was not altered this may have caused some weaknesses. But overall these results are pretty accurate for an AP statistics assignment.