Kelsey & Sarah's project

Does whether or not teens pay for their own gas affect how much they drive?=

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 he results of this study.

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The purpose of this study was to deter= mine, using statistical procedures, whether or not there was a correlation between teens who pay for their own gas and how much they drive. At the start of the study, it was thought that there would be an association. The randomly selected sample consisted of 36 Tates Creek High School juniors= . Each student was initially asked whether or not they paid for their own gas. The= n, they were given three categories of how much they drove and asked to put themselves in one of the three categories. These categories were: I drive to school; I drive to school and work; I drive everywhere. After the collectio= n of data was completed, the data was arranged in a two-way table. When finding = the expected values, it was found that the data did not meet all assumptions. Therefore, we combined the “school” and “school and work” categories to make one category: I drive to school and/or work.= A chi-square test of association was then carried out. The results of the stu= dy were extremely significant in favor of the null hypothesis. The statistical evidence was also strongly against the researcher’s first thoughts. However, please keep in mind the previously stated disclaimer that these re= sults are not set in stone.

Meth= odology

&= nbsp; As gas prices continue to rise, we are all beginning to closely monitor and re= duce our gas usage. Teenagers, unlike most adults, do not have a seemingly endle= ss supply of money to spend on their gas. This dilemma is what brought the researchers to the questions: Do teens have to pay for their own gas, or no= t? And does that effect how much they drive?

&= nbsp; The first step in carrying out this statistical study was selecting a sample. T= he sample was obtained by first acquiring a list of all juniors at Tates Creek High School. This l= ist was then numbered numerically from 1 to 366 and the researchers used the ra= ndom integer generator to randomly select 75 names. Because a list of students w= ho have school parking permits was not available, the researchers were require= d to ask the individuals whether or not they drove before proceeding with the ot= her questions. Of the 75 individuals selected, the first 36 to complete the sur= vey were the sample used.

&= nbsp; After collecting all data, counts were made and the results were put into a two-w= ay table for analysis. The researchers used the data in the two-way table to f= ind the expected values of each category. The expected values were used to find= c². Then, c² was used in combination with the degr= ees of freedom to find the p-value in Table E. Based on our p-= value, we were able to conclude that it would not be correct to reject H_0.

Data=

Init= ial Data that did not fit assumptions:

Drives: à<= /span>	Everywhere	School	School and Work	Row Total:
Pay for gas	20 E=3D19.25	0 E=3D.58333	1 E=3D1.1667	21
Not pay for gas	13 E=3D13.75	1 E=3D.41667	1 E=3D.83333	15
Column Total:	33 &nbs= p;	1	2	Table Total: 36

Fitted Data:

Obse= rved Counts:

Drives: à<= /span>	Everywhere	School and/or work=	Row Total:
Pay for gas	20 (#1)*	1 (#2)*	21
Not pay for gas	13 (#3)*	2 (#4)*	15
Column Total:	33	3	Table Total: 36

Expe= cted Counts:

Drives: à<= /span>	Everywhere	School and/or work=
Pay for gas	19.25	1.75
Not pay for gas	13.75	1.25

*These numbers are used to denote which expected value is being calculated

Work=

Assumpti= ons:

üA= ll expected counts are > 1

üN= o more than 20% of the expected counts are < 5

Hypothes= es:

H₀: There is no association= between teens who pay for their gas and the amount of driving they do.<= /o:p>

H_a: There is an association= .

E=3D (row total) (column total)

= Table total

E_#1=3D (21) (33) =3D 19.25 E_#2=3D (21) (3) =3D 1.75 = E_#3=3D (15) (33) =3D 13.75 E_{#4=3D (15)(3)
=3D1.25}

= (36) = &nb= sp; = (36) = &nb= sp; = (36) = &nb= sp; (36)

df =3D (# rows – 1) (# columns – 1) =3D (2-1) (2-1) =3D (1) (1) = =3D 1

c² =3D <= span style=3D'mso-spacerun:yes'> (O – E)²

c² =3D (20 – 19.25)<= sup> 2 + (1 – 1.75) ² + (13 – 13.75)<= /u> ² + (2 – 1.25) ²=3D .841558

&= nbsp; 19.25 = 1.75 = &nb= sp; 13.75 = &nb= sp; 1.25

Now that we= have the c² value, we use this and the degrees of freedom to find the p-value in Table E.

p-value =3D .3589

Conclusi= on:

&= nbsp; Because our p-value is .3589, which is much greater than a =3D.05, we fai= l to reject H₀ in favor of H_a. This means that there is no association between whether or not teenagers pay for their gas and how much= they drive.

Initial Data:

Fitted Data:=

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