1. IB Math Studies Internal Assessment:
Shoe Size and Height
School Name: International School of Bangkok
Date: November 2010
Course: IB Math Studies
2. Statement and Plan of Task:
In this assessment I will investigate the relationship between shoe size and height.
For this topic I have collected data from students in my age group, which is 17 to 18
years old. I collected fifteen shoe sizes and height for each gender. My task to is to
find patterns, which reveal how they are correlated, and the chi-squared test will
prove how significant the correlation is. In the end I will compare female and male
results to see how the correlation results differ or if they are exactly the same.
Hypothesis:
I believe that the relationship between shoe size and height is significant. The larger
shoe size is the taller a person will be.
The Measurements:
I have converted all the height measurements to centimeters and collected all shoe
sizes in by American standards.
11. CHI SQUARED TEST
MALE
Null Hypothesis- Height and shoe size are independent of each other.
Alternative Hypothesis- Shoe size is dependent of height.
Observed Frequency ( ):
Height (cm) 9-9.5 10-10.5 11-11.5 12-12.5 Total
161-170 1 2 0 0 3
171- 180 1 4 1 2 8
181-190 0 1 3 0 4
Total 2 7 4 2 15
Expected FREQUENCY ( ):
Height (cm) 9-9.5 10-10.5 11-11.5 12-12.5 Total
161-170 (2 x 3)/15=
.4
(7 x 3)/15=
1.4
(4 x 3)/15=
.8
(2 x 3)/15=
.4
3
171-180 (2 x 8)/15=
1.067
(7 x 8)/15=
3.733
(4 x 8)/15=
2.133
(2 x 8)/15=
1.067
8
181-190 (2 x 4)/15=
.533
(7 x 4)/15=
1.867
(4 x 4)/15=
1.066
(2 x 4)/15=
.533
4
Total 2 7 4 2 15
12. Calculated Chi Squared
- ( - ) ( - ) /
1 .4 .6 0.36 0.9
2 1.4 .6 0.36 0.9
0 .8 -.8 0.64 0.8
0 .4 -.4 0.16 0.4
1 1.067 0.067 0.0045 0.0042
4 3.733 .267 0.0713 0.0191
1 2.133 -1.133 1.284 0.602
2 1.067 .933 0.870 0.815
0 .533 -.533 0.284 0.533
1 1.867 -.867 0.752 0.4027
3 1.067 1.933 3.736 3.501
0 .533 -0.533 0.284 0.533
9.41
Degree of Freedom = (row -1) x (column -1)
= (3-1) x (4-1)
= 6
With the significant level of 5% Chi Squared from the table equals to 12.59. The
calculated result is 9.41 while the table result is 12.59. This means that the null
hypothesis is accepted, meaning that height and shoe size are independent of each
other.
13. FEMALE:
Null Hypothesis- Height and shoe size are independent of each other.
Alternative Hypothesis- Shoe size is dependent of height.
Observed Frequency ( ):
Height
(cm)
5-5.5 6-6.5 7-7.5 8-8.5 9-9.5 Total
141-150 1 0 0 0 1 2
151-160 0 1 3 0 0 4
161-170 0 0 3 1 2 6
171-180 0 0 1 1 1 3
Total 1 1 7 2 4 15
Expected FREQUENCY ( ):
Height
(cm)
5-5.5 6-6.5 7-7.5 8-8.5 9-9.5 Total
141-150 0.133 0.133 0.933 0.267 0.533 2
151-160 0.267 0.267 1.867 0.533 1.067 4
161-170 0.4 0.4 2.8 0.8 1.6 6
171-180 0.2 0.2 1.4 0.4 0.8 3
Total 1 1 7 2 4 15
14. Calculated Chi Squared
- ( - ) ( - ) /
1 0.133 0.867 0.752 5.65
0 0.133 -0.133 0.017 0.127
0 0.933 -0.933 0.87 0.932
0 0.267 -0.267 0.071 0.265
1 0.533 0.467 0.218 0.409
0 0.267 -0.267 0.071 0.265
1 0.267 0.733 0.537 2.01
3 1.867 1.133 1.283 0.687
0 0.533 -0.533 0.284 0.532
0 1.067 -1.067 0.284 0.266
0 0.4 -0.4 1.138 1.067
0 0.4 -0.533 0.16 0.4
3 2.8 0.2 0.284 0.101
1 0.8 0.2 0.04 0.05
2 1.6 0.4 0.16 0.1
0 0.2 -0.2 0.04 0.2
0 0.2 -0.2 0.04 0.2
1 1.4 -0.4 0.16 0.114
1 0.4 0.6 0.36 0.9
1 0.8 0.2 0.04 0.05
14.325
Degree of Freedom
= (4-1) x (5-1)
= 12
With the significant level of 5% Chi Squared from the table equals to 21.0. The
calculated result is 14.325 while the table result is 21.0. This means that the null
hypothesis is accepted, meaning that height and shoe size are independent of each
other.
15. BOTH:
Null Hypothesis- Height and shoe size are independent of each other.
Alternative Hypothesis- Shoe size is dependent of height.
Observed Frequency ( ):
Height
(cm)
5-6.5 7-8.5 9-10.5 11-12.5 Total
141-150 1 0 1 0 2
151-160 1 3 0 0 4
161-170 0 4 5 0 9
171-180 0 2 6 3 11
181-190 0 0 1 3 4
Total 2 9 13 6 30
Expected FREQUENCY ( ):
Height
(cm)
5-6.5 7-8.5 9-10.5 11-12.5 Total
141-150 0.133 0.6 0.867 0.4 2
151-160 0.267 1.2 1.733 0.8 4
161-170 0.6 2.7 3.9 1.8 9
171-180 0.733 3.3 4.767 2.2 11
181-190 0.267 1.2 1.733 0.8 4
Total 2 9 13 6 30
16. Calculated Chi Squared
- ( - ) ( - ) /
1 0.133 0.867 0.752 5.65
0 0.6 -0.6 0.36 0.6
1 0.867 0.133 0.018 0.021
0 0.4 -0.4 0.16 0.4
1 0.267 0.733 0.537 2.011
3 1.2 1.8 3.24 2.7
0 1.733 -1.733 3.003 1.733
0 0.8 -0.8 0.64 0.8
0 0.6 -0.6 0.36 0.6
4 2.7 1.3 1.69 0.626
5 3.9 1.1 1.21 0.31
0 1.8 -1.8 3.24 1.8
0 0.733 -0.733 0.537 0.733
2 3.3 -1.3 1.69 0.512
6 4.767 1.233 1.52 0.319
3 2.2 0.8 0.64 0.291
0 0.267 -0.267 0.071 0.267
0 1.2 -1.2 1.44 1.2
1 1.733 -0.733 0.537 0.31
3 0.8 2.2 4.84 6.05
26.933
Degree of Freedom
= (5-1) x (4-1)
= 12
With the significant level of 5% Chi Squared from the table equals to 21.0. The
calculated result is 26.933 while the table result is 21.0. Because this result is
greater than the chi squared from the table, the null hypothesis is rejected. Which
means that height and shoe size are dependent of each other.
17. Conclusion
After analyzing the gathered date and finding the R values and Chi squared
test it can be concluded that height and shoe size are correlated. It is not a very
strong correlation but with results of 0.38 for male, 0.33 for female and 0.577 for
both the correlation is shown. In the graphs it is also very visible to see the
correlation and because the point are not extremely spread out the it is shown that
the correlation is somewhat strong. Chi squared showed us that the null hypothesis
was accepted for both male and female but when it came to testing both, the null
hypothesis was rejected.
