Natalie, Cassie, & Corey's project

Is the Tates Cr= eek High School proport= ion of smokers the same as the nationwide proportion of= High School smokers?

May 18, 2005

Natalya = Lozovoy

Cassie Starr

Corey Bush<= /span>

Disclaimer:

            = 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.

Abstract:

            In our study, we want to see if the national statistics for high school smokers     ( 21.9 % from American Cancer Society available at http://www.cancer.org/docroot/COM/c= ontent/div_Northwest/COM_5_1x_Youth__Tobacco.asp ) matches the proportion of student smokers at Tates Creek. Our sample population is the entire population of TCHS, and we systematically selected every 16^th student in the school. The systematically chosen students were given a survey, which asked them if they currently smoked 5 or more cigarettes a week. Our definition of smoking was= 5 or more cigarettes a week, but we are not aware of what the American Cancer Society defined smoking as. Keep in mind that this could slightly sway our results. In this study our main goal is to determine whether or not there w= as a statistically significant difference between the national proportion of smo= kers and the TCHS proportion of smokers. We are going to use a One Proportion Z-= test to compare these proportions. We are expecting the proportion of TCHS smoke= rs to be smaller than the national proportion, because if students are surveye= d by other students, they are more likely to lie in their results because of peer pressure.

Methodology:<= /b>

            = The American Cancer Society claims that 21.9 % of American high school stud= ents smoke. This could be true overall, but the results may vary differently from high school to high school. Is that true for Tates Creek High School?

To find th= e answer to this question we first conducted a survey. We obtained an alphabetical l= ist of students in each grade. Starting with freshmen and finishing with senior= s, we chose every 16^th student to participate in our survey. We wan= ted a sample of a 100 students, and in order to equally choose enough students = from each grade, we divided the number of students in our high school by 100, so tha= t is why we did every 16^th student.

This is what our survey = looked like:

___________________________= __________________________________________

Do you currently smoke? ( 5 or more cigarettes a week)

Yes

No

In order to encourage honest answers, we explained to the students we surveyed that this study is comple= tely anonymous, and as they filled out the survey, we turned our backs.

Due to a limited time frame= for our data gathering, we could not survey every single student we planned. Some students were absent or unavailable. We surveyed 80 students.

Exploratory Data Analysis

Raw Data:=

Answers:

Yes

No

Do you smoke?

8

72

Inference:

&nb= sp;          H-naug= ht: p =3D .219 (The TCHS proportion of smokers is 21.9%)

            H-a:         p ≠ .= 219 (The TCHS proportion of smokers is NOT 21.9%)

Assumptions:<= /u>

np≥10 &n= bsp;           80(= .219) =3D 17.52     &nbs= p;   n =3D sample population

n(1-p) ≥10       80(1-.219)=3D62.48        p =3D parameter (proportion of national smokers)

            SRS (every 16^th person alphabetically)

            The population is at least 10 times as large as the sample (80x100 =3D 800 ther= e are more than 800 students at Tates Cr= eek High School)

One proportion z-test:

Z =3D -2.5736

p-value= =3D .0101

Conclusion:

            = Since the p-value of .0101 is smaller than the alpha lever of .05, we have statistically significant evidence to reject H-naught in favor of H-a. This means that the TCHS proportion of smokers is significantly different from national statistics. Before replicating these results, keep in mind that th= e small sample size and possible response bias and some non-response (students who = were absent) may have somewhat influenced the results of this study. Since our definition of smoking was 5 or more cigarettes a week, and American Cancer Society’s definition is unknown, this may somewhat influence the resu= lts also. Response bias may also be a big issue, since some students may have b= een afraid that the surveyors would know they smoke.