Parking

 

An observational study of illegal student parking at Tates Creek Senior High School

 

 

 

 

 

By:

 

CRISTA DITTERT & MICHAEL COLLINS

 

 

May 2004

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.

 

 

The purpose of this study was to draw inference upon the proportion of legally parked cars in the Tates Creek High School student parking lot (TCHSSPL).  Casual observation by the researchers prior to the actual commencement of this study suggested that a higher proportion of cars may be illegally parking than expected.  This study was approached with the hope of proving this theory. Actual scientific observation was carried out by calculating an expected proportion of legally parked cars, randomly sampling thirty cars from TCHSSPL, and observing the sample proportion of legally parked cars.  This process was repeated at the same time each day for three days.  An average proportion was then calculated, along with the sample standard deviation, and a one sample t test was carried out for the purpose of inference.  This test produced statistically significant evidence in favor of the researchers’ initial suspicion that a higher proportion of illegally parked cars exists than expected, suggesting the results of this study are heavily conclusive.  This is stated with respect to the above disclaimer, which states that the validity of such observational studies must be questioned.  Nonetheless, it is hoped that the following report can serve as a strong voice in the issue of student parking at Tates Creek High School.

 

As the end of the school year approaches, it is common knowledge that it becomes more and more difficult to find a place to park in the Tates Creek student parking lot.  There are exactly 302 parking spaces designated for students, and the administration of Tates Creek High School is legally only able to distribute 332 student parking permits.  Having reached the limit of 332 earlier in the school year, no new parking permits have been given out for several months.  Why, then, does it become increasingly difficult for a student to acquire appropriate parking as the school year progresses?  The researchers hypothesized that illegal student parking was a contributing factor, and decided to focus on this factor in this statistical study.  The question then became, is the mean proportion of cars parked legally in the student parking lot at Tates Creek High School actually lower than expected?      

 

In order to conduct a statistical study on the proportion of cars parked legally, it was first necessary to calculate the expected proportion to be used in the original hypothesis.  Although this expected proportion can be argued, one would initially expect 100% of cars in designated student parking spots to have student permits.  However, school visitors – who do not have parking permits, and may or may not be aware of designated visitor parking spots – must not be overlooked; they unknowingly park illegally, and therefore, must not be counted against the student population.  So, to explain this variable, eight visitor login sheets (from the visitor login binder in the TCHS main office) were randomly selected: six from August – January and two from more recent weeks.  (This was done to make sure recent visitor activity was well represented.)  From these sheets, the average number of visitors in the building at any given hour was calculated.  This number came out to be approximately five.  (See below for actual figure).  So, to calculate the expected proportion of legally parked cars, it was assumed that five visitors were illegally parked in student parking spots at any given time.  (It must be noted here that the researchers are fully aware that this figure may be regarded as “generous,” and that it may be thought of as highly unlikely that all five visitors are illegally parked in student parking spots, when there are, in fact, clearly designated visitor parking spots.  The researchers openly acknowledge this and provide as explanation the claim that it was, under the constraints of the observational study, quite impractical to pursue a more accurate figure for the visitor variable.  Furthermore, it is strongly suggested that this aspect be further investigated, should this study be replicated by other persons.)  Next, the total number of student parking spaces (302) was observed.  With the acquisition of these figures, all of the variables necessary to compute the expected proportion were available, and thus the expected proportion was computed as follows:

 

[(total number of student spots) – (visitor factor)] ¸ (total number of student spots) = expected proportion

and \

(302 – 4.8188) ¸ 302 = 0.9840

Next the specifics (such as sample size, selection of cars to be observed, and time of observations, etc.)  of our experimental design were to be decided.  First a figure of n=30 cars was decided upon for each sample.  Due to time constraints, there was only the opportunity to collect data on three different days.  The decision was made to take one sample per day at a randomly selected time during the school day (using this same randomly selected time each day).  It was hypothesized that the data collection process would take approximately 30 minutes per sample, so the school day (beginning at 8:30am and ending at 3:20pm) was divided into 14 half hour units.  These units were numbered from 1-14 (for example 8:30am-9:00am = 1, 9:00am-9:30am =2, 9:30am-10:00am = 3, etc), and the random integer function (randInt) on a TI-83 Plus calculator was used to randomly select a digit from 1-14.  The digit 4 was obtained, therefore making the data collection time each day 10:00am-10:30am.  The next step was to obtain the actual samples.  There are 302 student parking spots which are numbered from 1-302.  To randomly select 30 cars each of the three days, the random integer function of a TI-83 Plus calculator was used once again. (Randomly chosen parking spots can be seen on the raw data sheets.)  At 10:00am on each of the three collection days, the researchers went to the student parking lot and recorded whether or not the cars parked in the 30 randomly chosen parking spaces had student parking permits (a different sample of 30 was taken each day).  If the automobile did not have a student parking permit, but rather a teacher parking permit, the car was observed as “legally parked. “

 

Here is a table of the raw data collected:

Date

 # cars parked legally

  # cars parked illegally

  Proportion of cars parked legally

5/17/2004

23

7

0.7666

5/18/2004

21

9

0.7

5/19/2004

19

11

0.6333

 

 

After the proportion of cars parked legally each day was calculated, those three values were averaged, giving x-bar = .6999.  The alpha level was set to a = .01.  The original hypothesis was m = .984 and the alternative hypothesis was m < .984.  Defining the symbols, m = the mean proportion of cars parked legally in the Tates Creek High School student parking lot.  Three different samples were taken, making n=3.  The one variable statistics were then run on this data using a TI-83 Plus calculator (1-Var Stats) to obtain the sample standard deviation (s = .06666).  Before running the t-test, assumptions had to be checked.  The first assumption is that the sample is a simple random sample (or SRS).  This assumption was met (refer back to sampling techniques).  Because n<15, the second assumption is that the data is normally distributed with no outliers.  A dot-plot of the data was constructed (shown below), proving that this assumption was met.  (One should note that t-distributions are robust, and even if the assumptions were violated, the p-value would be affected very little). 

 

 

 

 

 

 

    Legally Parked Cars

 

 

 

 

 

 

 

 

 

0

0.25

0.5

0.75

1

 

 

 

 

Proportion

 

Next the one-sided, one sample t-test was performed.  Here are the calculations:

 

t = (x-bar - m) ¸ (s/(n^1/2)) = (.6999 - .984) ¸ (.06666/(3^1/2)) =  -7.3786

 

To check the results, the one sample t-test was run on a TI-83 Plus calculator.  The p-value corresponding to the t-test statistic was found to be p = .008938.  Because the p-value is .008938, which is less than a=.01, it is reasonable to reject Ho, the original claim that the mean proportion of cars parked legally in the Tates Creek High School student parking lot is equal to .984, in favor of Ha, the claim that this mean proportion is less than .984.  The p-value lets one know the probability of randomly attaining this sample if Ho were, in fact, true.  Because the p-value, in this case, is so low, there is statistically significant evidence to reject the original claim. 

However, it is important to note that confounding and lurking variables could have been present within this study.  For example, all school awards were taking place when the Wednesday (5/19/04) sample was observed.  Many parents and other relatives attended this awards ceremony, and it is likely that they parked in spaces allotted for students.  Also, these samples were all taken at the end of school year when many of the underclassmen, who were ineligible for parking permits earlier in the year, obtained their driver’s licenses and drive to school regardless.