Stats Project 2007

Is there a relationship between a student’= s GPA and their self-esteem?

Hannah Wheeler

Katherine Oliva

AP Statistics Project

Spring 2007

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 us= e or report the results of this study.

Abstract

&= nbsp; The purpose of this study was to see if there was a relationship between a student’s grade point average (GPA) and self-esteem. The expected outcome is that stude= nts with lower GPAs also have lower self-esteem. This is expected because if one ha= s a lower self-esteem then he/she won’t try as hard to get better grades.=

This surve= y was done on the freshman population of Tates Creek High School. To perform the survey, a simple random sample (SRS) was taken of the freshman class. All of the st= udents were given a survey asking for their GPA and two questions concerning self-esteem.

A sample mean was the calculated, a= long with a sample standard deviation, and a t-test for linear regression was th= en carried out comparing GPA to self-esteem.

A major fa= ctor into the results of this test was non-response bias. Out of the 75 students that the researchers attempted to contact, only 37 responded.

= ;

Methodo= logy

A roster o= f the freshman class at Tates Creek High School during May 2007 was obtained and each student was assigned a number from 1 to 461. The random integer generator on the graphing calculator was used to acquire 75 different numbers. Those students whose numbers appea= red were then selected to be surveyed.

The purpose of the survey was to co= mpare a student’s GPA and self-esteem.&nbs= p; The students were located by their schedules and the researchers gave them the surveys. The surveys= were done completely anonymous by placing those completed without a name into a large envelope full of other surveys.

The questi= ons on the survey to be completed were:

1) What is= your GPA?

2) How do = you feel about yourself? Rate from 1-5= , 1 being very poor and 5 being &nb= sp; very good

3) How do = you feel about your appearance? Rate f= rom 1-5, 1 being very poor and 5 being very good

The survey= stated not to put their names on it and when the students took the survey, the researchers didn’t watch.

= ;

Raw = Data

Subject	GPA	Yourself	Appearance=	Average
1	3	5	4	4.5
2	3.7	4	3	3.5
3	3	3	3	3
4	2	4	3	3.5
5	3.5	5	5	5
6	3.8	3	3	3
7	3.2	5	5	5
8	3	4	3	3.5
9	3.3	5	5	5
10	4	5	5	5
11	3.3	4	4	4
12	3	3	2	2.5
13	3.6	4	4	4
14	2.5	4	4	4
15	1	4	4	4
16	2.5	3	4	3.5
17	2.5	4	4	4
18	3.25	4	4	4
19	2.5	5	4	4.5
20	2.3	5	5	5
21	3.5	4	4	4
22	3.5	5	3	4
23	3.1	5	4	4.5
24	1.9	5	5	5
25	3.7	3	4	3.5
26	1	5	5	5
27	3.5	5	5	5
28	3	5	4	4.5
29	3.5	4	4	4
30	2.6	4	4	4
31	3.6	4	4	4
32	2.75	4	4	4
33	2	3	4	3.5
34	3.4	4	3	3.5
35	2.6	5	5	5
36	3.2	5	5	5
37	3.4	5	4	4.5

= ;

Assumptions

Ö Observations are independent

Ö True relationship is linear

Ö The standard deviation of the response varia= ble is the same everywhere about the true line (see residual plot)

Ö Response variable varies normally.

Residual Plot:

Residuals Versus the = Fitted Values

(Response is Self-Esteem)

<= ![endif]>

Scatter plot with LSR= L:

1

2

4

3

Scatter plot of GPA vs. S= elf-Esteem &= nbsp;

G

P

A

<= ![endif]>

= &nb= sp; 3 &= nbsp; &nbs= p; 4&= nbsp; &nbs= p; 5

&= nbsp; &nbs= p; &= nbsp; Self-Esteem

Inference:

Ho: &= #946; =3D 0 (There is no relationship between GPA and self-esteem.)

Ha: β ≠ 0 (There is a relationship betwe= en GPA and self-esteem.)

β<= /span> is defined as the true slope of the relationship between GPA and self-esteem

Test:

t =3D b – β<= /u> =3D -.1024 - 0 =3D -.5777

SEb = &nb= sp; SEb

p =3D .56= 72

Conclusion

&nb= sp; Because the p-value gives p=3D .5672 at the α =3D .= 05 level, our data is not statistically significant and we therefore retain Ho that there is no relationship between GPA and self-esteem.

&= nbsp; Due to a small sample size and a large non-response bias, it is important to remember that this data may not be reliable. Also, sense the surveys were anony= mous many students may not have given accurate answers to the questions. Observer bias may be present as we= ll because the researcher was standing nearby while the survey was being filled out. In addition, students ma= y not have been knowledgeable about their GPAs and only freshmen were surveyed. These results should not be publis= hed without replication.