Who Has Been In More Car Accidents In The Junior And Senior Classes At Tates Creek High School: Males Or Females?

 

 

 

 

 

 

Felicia Baldwin

Paul Schultz

Andrew Schwartz

B2      AP Statistics

5/21/03

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 - 

The goal of this study is to determine who gets into more car accidents at Tates Creek High School: males or females.  For this survey, an accident is defined as anything from a fender-bender to totaling a car.  No previous data was found on whether males or females get into more accidents, but it is believed that males and females get into the same amount of accidents.  Males tend to drive more haphazardly than girls, which is why guys have higher insurance rates.  Another thing to consider is the personality of the driver.  Generally, girls are perceived to be passive drivers and guys are perceived to be aggressive drivers.  This perception of aggressive driving by men could result in men having more accidents than women, but it does not necessarily mean women do not get into less accidents because of their passive driving.

This survey is conducted to determine whether or not there is statistical evidence in order to prove that male and females at Tates Creek High School do not get in the same number of car accidents. In order to prove this, random samples of 100 seniors and juniors are taken, both male and female, to fill out our survey.  To create the random sample, a class list was obtained for the seniors and juniors at Tates Creek High School and each student was given a number.  Then by using a random number generator, 100 students were selected.  Not all 100 students responded; therefore, the final number of students selected was 63; 25 females and 38 males.  At Tates Creek High School there are 354 females and 383 males in the junior and senior classes.  The sample sizes of 25 and 38 are around one tenth of the populations that is required to conduct a significance test on proportions.  Tates Creek High School’s juniors and seniors were chosen because very few freshmen and sophomores can drive, and it would be pointless to survey those who cannot drive.  It would also be impossible to survey one tenth of the populations of males and females in Lexington because the populations are so large. 

 

 

Methodology -

            To conduct this survey, a list of all the juniors and seniors attending Tates Creek was acquired from the Counseling office.  The junior and senior lists, which contained males and females, were combined to make one list that was 738 students long.  Then, each junior and senior was assigned a number, such as 1, 2, 3, ect., until all the students were numbered.  Next, the random number generator of a TI-83 graphing calculator was used to randomly select the individuals who would receive the survey.  The number produced by the random number generator corresponded to a number assigned to a junior or senior.  That person would be one of the subjects in the survey.  The random number generation was run 100 times, but only 63 students responded; 25 female and 38 male.  This is appropriate because the sample sizes of 25 and 38 subjects are around 1/10 of the population sizes.  In other words, the populations are more than 10 times the size of the samples.

 

Exploratory Data Analysis -

 

 

 

 

No Accidents

# Of Who Have Been In Accidents

Total # Of Accidents

Total # Of Subjects

Males

12

23

41

38

Females

13

15

31

25

 

 

Analysis and Inference -

Assumptions :  

There are two independent SRS’s from the population of interest.

            We used a random number generator to obtain our subjects.

The populations are at least ten times as large as the sample.                  

The population of males was 384, which was ten times the sample of 28 that we took.  The population of females was 354, which was ten times the sample of 35 that we took.

 

            For this Z-test, population 1 is males and population 2 is females.  The sample proportions that have been in accidents are

                                                p1=23/38=.6053  (males)

                                                p2=15/25=.6000  (females)

-n1(p1) > 5       and      n1(1 – p1) > 5

            38 (.6053 ) > 5            38 (.3947 ) > 5

            = 23.0014                    = 14.9986

            n2(p2) > 5         and      n2(1 – p2) > 5

            25 (.6000 ) > 5            25 (.4000) > 5

            = 15                             = 10

            n1 = number of males in the population.

            n2 = number of females in the population.

            p1 = proportion of males that have been in car accidents

            p2 = proportion of females that have been in car accidents

                                     

           

That is, about 60.53% of males have been in car accidents while 60% of females have been in car accidents.  This survey hopes to show that males and females of the junior and senior class at Tates Creek High School do not get into the same number of car crashes.  So it is a two-sided alternative:

                                                H0: p1 = p2

                                                Ha: p1 ¹ p2

To do a test, the next step was to standardized p1-p2 to get a z statistic.  To do this, the single population parameter p was estimated.  This is called the pooled sample proportion.  It is

                        p= count of successes in both samples combined      = .6032

                           count of observations in both samples combined

To test the hypothesis, H0: p1=p2, first find the z statistic.

                        z=     p1 – p2_____       =  .6053-.6000                            = .0418

                           Öp(1-p)(1/n1 + 1/n2)     Ö(.6032)(.3968)(1/38 + 1/25)

 

Then use the Z-table to find the p-value, which is .9667.

 

Conclusion –

            The p-value=.9667, which is greater than alpha=.05, so the data is not statistically significant; therefore, one should fail to reject H0 in favor of Ha.  In other words, there is not significant evidence to reject H0.  This means that males and females in the junior and senior classes at Tates Creek High School get into accidents about the same amount.  The p-value of .9667 means that there was a 96.67% chance that the data collected was by chance, and H0 is true.