IB Math Studies Internal Assessment:

Shoe Size and Height

School Name: International School of Bangkok

Date: November 2010

Course: IB Math Studies

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.

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

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.

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

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.

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

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.

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.