AP Statistics Project 2006=

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

By: Max Clark, J.D. Sims, and Kent Mulberry

ABSTRACT

The purpose of this study was to prove any relation= ship between the grade level of a student and the common knowledge that they ret= ain at Tates Creek High School (TCHS). Since this study is concerned about comm= on knowledge or as some might call it “Street Smarts,” the common knowledge level should not be affected by their grade level. This study was conducted in hopes of proving that common knowledge is not related to a student’s grade. A survey containing 5 questions that would be consid= ered “common knowledge” was given to each of 120 randomly selected students at TCHS, 60 lower classmen and 60 upperclassmen. A sample mean was then calculated, along with a sample standard deviation, and a 2-sample t-t= est was then carried out for the purpose of inference. This test proved to be n= ot statistically significant, leaving evidence that students at a higher-grade level at TCHS do not have more common knowledge. This is stated with respect to the above disclaim= er, which states that the validity of such observational studies must be questioned. It is still hoped that these results can be used to prove that common knowledge is not related with a person’s grade level.

METHODOLOGY

    &= nbsp;     Dumb people have always been a comical fascination for many people in the United States. A popular segment on the Tonight Show with Jay Leno shows how dumb people in America really are. He randomly picks people on the streets of Los Angeles for the simple, common knowledge question that he asks. What about = the people at Tates Creek High School? Do the older students, those who have be= en in school longer and have had more time to learn have more common knowledge than the younger students? To completely randomize the sampling process, it= was necessary that the subjects were randomly selected using a random number generator from a list of all of the upperclassmen in school, and a list of = all the lower classmen in school. The lower classmen were numbered from 1 to 880 and the upperclassmen were numbered from 1 to 672. A TI-83 calculator was u= sed to do the random integer selecting. The purpose is to compare the common knowledge of upperclassmen to the common knowledge of lower classmen. To do this, we stratified our sample and we took 60 subjects from both the upperclassmen and the lower classmen. The freshmen had the same opportunity= to be picked as the sophomores, and the juniors had the same opportunity to be picked as the seniors. First, each student’s schedule had to be looke= d up on STI so that they may be sampled during their first block class on B day.= The samplers each went to a classroom and asked for all of the students involve= d in the study to come out into the hallway with a pencil. The subjects were fir= st given a student release form so that their data could be used, and then they were handed the survey. They were asked to first put their grade on the sur= vey before beginning so that they could be assorted later. Once they finished, = the

survey and release form were collected and the students returned to class.

# questions correct

Upper classmen

Lower classmen

0

0

0

1

3

0

2

4

12

3

16

17

4

14

7

5

4

7

The Box plot for the upperc= lassmen is the top plot and the box plot for the lower classmen is the bottom plot.=

Questions Given To Subje= cts:

How many states are in the continental U.S? A: 48

Who was the first president of the United States? A: George Washin= gton

How many days are in a leap year? A: 366

What is the capital of Kentucky? A: Frankfort

Who is the vice president of the United States? A: Dick Cheney

ANALYSIS

Hypothesis:    =        Ho: µLowerclassmen=3DµUpperclassmen

    &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;      Ha: µLowerclassmen<µUpperclassmen<= /p>
Where µ is the mean s= cores of the common knowledge surveys.

Assumptions:

1.&n= bsp;     Independent SRS’s

2.&n= bsp;     Both sets of observations are normally distributed = (One should note that t-distributions are robust, and even if the assumptions we= re violated, the p-value would be affected very little)

   &nb= sp;            =             &nb= sp;

t=3D .3697            =             &nb= sp;            =           df=3D81.8514<= span style=3D'mso-tab-count:3'>        &= nbsp;           &nbs= p;            p-value=3D.3563

Since our p-value (.3563) i= s larger than the generally accepted α=3D .05 level, our data is not statistica= lly significant and we therefore retain Ho, meaning that the upperclassmen and = the lower classmen have about the same mean number of correct answers.

Our study = may have contained some bias that was not easily controlled. Since these surveys were anonymous, many people may not have taken it seriously and may not have giv= en their best effort to get all of the questions correct. Also, in a few cases there could have been cheating among the subjects when the person who administered the surveys was not looking. This could have been remedied by having taken each student out one at a time so that cheating wasn’t possible. The reason this wasn’t done was because it was not practica= l to do so. The biggest bias introduced into this study is the non-response bias from sampled students who were absent. The sample size for each group regar= dless turned out about the same anyways.

# questions correct	Upper classmen	Lower classmen
0	0	0
1	3	0
2	4	12
3	16	17
4	14	7
5	4	7