Kari, Katie, Robbie

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 min= d if you use of report the results of this study.

Abstract

The purpose of this study is to determine if having a sibling influences a person’s grades. Students with older siblings may be inclined to do better in school simply because of the desire to be superior.

This survey was conducted on the population of Tates Creek High School’s student body. This is supposed to be representative of today’s high school students. The Test we preformed was a c² (chi-squared test). This test = helps determine whether the hypothesis is statistically significant. This test al= so helps determine which factor has the most influence on the outcome.

Methodology

Do older s= iblings influence the grades of their younger brothers and sisters?

In this study students were randomly selected by assigning numbers and using a random number generator. After selecting th= ese students the students were surveyed during their first block B-day class. T= he students were asked to sign a subject release form and then take the survey= as truthfully as possible. In total 100 students were selected, however only 81 could be reached making the sample size (n) equal to 81. Unfortunately anot= her problem presented itself after the surveys were completed. Some of the categories observed resulted in zero subjects, violating the assumption tha= t No more than twenty percent of expected counts could be less than five. Theref= ore the student’s grades were blocked into two categories, above average students and average/below average students (those who excel and those who “just get by”).

Exploratory

Analysis

Assumptions

All individual expected counts are at least 1.
No more than 20% expected counts are < 5.

&nbs= p;

Hypothesis

H₀: There is no association between students with older siblings and their grades.

H_a: There is an association between students with older siblings and their grades.

Observed

<= o:p>	<= o:p>	S= tudents Grades	<= o:p>	<= o:p>	<= o:p>	<= o:p>
S= ibling	<= o:p>	A=	B=	C=	D=	F=	T= otal
<= o:p>	A=	7	7	2	0	0	16
<= o:p>	B=	2	9	5	1	0	17
<= o:p>	C=	2	7	10	1	0	20
<= o:p>	D=	0	1	1	0	0	2
<= o:p>	F=	0	0	1	1	0	2
No Sibling	4	9	9	2	0	24
T= otal	<= o:p>	15	33	28	5	0	81

&= nbsp; We were unable to use the data in this state because it violated assumption #2; therefore we blocked the data into the two groups of above average and average/below average (shown below).

Observed

<= o:p>	<= o:p>	<= o:p>	S= tudents	<= o:p>
S= ibling	<= o:p>	A= -B	C= -F	t= otal
<= o:p>	A= -B	25	8	33
<= o:p>	C= -F	10	14	24
No Sibling	13	11	24
T= otal	<= o:p>	48	23	81

Expected

<= o:p>	<= o:p>	<= o:p>	S= tudents
S= ibling	<= o:p>	A= -B	C= -F
<= o:p>	A= -B	19.556	13.444
<= o:p>	C= -F	14.222	9.778
No Sibling	14.222	9.778

Expected<= /p>

E =3D <= u>(row total) (column total)

&= nbsp; (table total)

&n= bsp;

E_#1=3D (48) (33) ≈ 19.556 E#2=3D (33) (33) ≈ 13.444 E_#3= =3D (48) (24) ≈ 14.222

= (81) = &nb= sp; = (81) = &nb= sp; = (81) = &nb= sp;

E_#4=3D (33)(24) ≈ 9.778 = E_#5=3D (48)(24) ≈ 14.222 &= nbsp; E_#6=3D (33)(24) ≈ 9.778

&nb= sp; (81) = &nb= sp; = (81) &= nbsp; &nbs= p; &= nbsp; (81)

Degrees of Freedom (DF)

DF =3D (Number of rows R= 11; 1) (Number of columns – 1)

DF =3D (3-1)(2-1)

DF =3D (2)(1)

DF =3D 2

&nb= sp;

Chi-S= quared

&nb= sp;

The sum = of the observed counts minus the expected counts all squared, then divided by the expected counts.

=3D (25-19.556) &= #8776;1.5158

&= nbsp; 19.556

=3D (8 - 13.444) &= #8776;2.2045

&= nbsp; 13.444

=3D (10 – 14.22= 2) &= #8776;1.2533

&= nbsp; 14.222

=3D (14 – 9.778= ) &= #8776;1.8232

&= nbsp; 9.778

=3D (13 – 14.22= 2) &= #8776;.1050

&= nbsp; 14.222

=3D (11 – 9.778= ) &= #8776;.1528

&= nbsp; 9.778

Sum ≈ 1.5158 + = 2.2045 + 1.2533 + 1.8232 + .1050 + .1528

=3D 7.055

To find = the p-value we use Chi-squared and the degrees of freedom in Table E (Chi-squar= ed distribution critical values).

P-value = =3D .02937

Concl= usion

&= nbsp; Since our p-value is .02937 we can conclude that at the a =3D .05 level our data is statistically significant. We can therefore reject H₀in favor of H_a. This means that there is an association between having an older sibling and you’re the grades you receive.

Some of the problems we encountered were the students not being able to be reach= ed which made our sample size smaller. Also the data violating the assumptions, which made us, have to block our data. If we were to do this again we would= I think it would be better if we had a larger sample size and have made our d= ata more reliable.

&nb= sp;