Presentation on theme: "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."— Presentation transcript:
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 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!
o 1769- First self-propelled car o 1886- Internal combustion engines developed o 1896- First road traffic death o 1997- Green cars
o Every 5 cars in CB South parking lot o More variables to decide from Color Type (Car, SUV, Truck, Other) Number of Doors
RedSilverGreenBlueWhiteBlackOtherTotal 2-Door Car 331042114 4-Door Car 6207577557 SUV 263453124 2-Door Truck 01010114 4-Door Truck 00001203 2-Door Other 10000012 4-Door Other 321320112 Total 15321213191510116
o Chose to this graph to display the overall results in a simple and general form o Majority of vehicles are cars o Few trucks, but may be different in population where more workers use trucks to transport heavy items
Color and Type o Stacked bar graph o Shows all variables o Silver 4- door cars are dominant o Blue has no 2- door cars, so in the population they must be minimal
o Chi- Square Test: Goodness of Fit o Uniform o Our Sample vs. North America o Chi- Square Test for Association: Color vs. Car Size o One Proportion Z Test for SUVs o One Proportion Z Interval for SUVs
o Assumed (we performed the test) o √ (all expected counts are 16.5714) o SRS o Sample size large enough that all expected counts are greater than or equal to 5
We found a website releasing the car colors of 2006 in North America from the DuPont Annual Color Popularity Report.website 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%.
Expected: Red - (.11)(116) = 12.76 Silver - (.32)(116) = 37.12 Green - (.04)(116) = 4.64 Blue - (.11)(116) = 12.76 White – (.19)(116) = 22.04 Black – (.13)(116) = 15.08 Other – (.11)(116) = 12.76 Observed: Red - 15 Silver - 32 Green - 12 Blue - 13 White - 19 Black - 15 Other - 10 H o : The observed frequency distribution of car colors fits the expected. H a : 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 …= 13.7952 df=6 α=.05
We reject H o in favor of H a 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). H o : The observed frequency distribution of car colors fits the expected. H a : The observed frequency distribution of car colors does not fit the expected.
State Two Independent SRS Sample size large enough that all expected counts ≥ 5 Check Assumed Does not check- we choose to proceed H o : Car color and size are independent. H a : Car color and size are dependent. RedSilverGreenBlueWhiteBlackOther Small9.18119.5867.3457.95711.6299.1816.1207 Large5.81912.4144.6555.0437.3715.8193.879 …=4.629 df=6 α=.05
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 color o Thought that it was more likely for a small, sporty car to be a flashy color like red rather than a large truck o Grouped our sample into two categories: o Small, for cars, and large, for SUVs, trucks, and other o Because 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. ***
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 H o : p=.3 H a : p<.3 State SRS np ≥10 n(1-p) ≥10 pop ≥ 10n Check Assumed 116×.3 ≥10 116×.7 ≥10 pop ≥1,160 We reject H o in favor of H a 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 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!
o Not every car in the parking lot is there everyday, so we probably missed some o We did not meet all the assumptions, but we continued with the tests o We should have picked the cars by using a software to randomize which cars we looked at by their spot number