Problem: What is the mean difference between the gold medals (x) and the silver medals
(y) of the 15 countries that have participated in the 2022 Olympics held in Beijing China?
Step 1:
Countries
Gold (x)
Silver (y)
(x1 - x̄1)
(x1 - x̄2)2
(y1 - ȳ1)
(y1 - ȳ2)2
Norway
16
8
10.94
1.20
2.94
8.64
Australia
1
2
-4.06
16.48
-3.03
9.36
Italy
2
7
-3.06
9.36
1.94
3.76
Japan
3
6
-2.06
4.24
0.94
0.88
USA
8
10
2.94
8.64
4.94
24.40
New
Zealand
2
1
-3.06
9.36
-4.06
16.48
Great
Britain
1
1
-4.06
16.48
-4.06
16.48
Canada
4
8
-1.06
2.56
2.94
8.64
China
9
4
3.19
15.52
-1.06
2.56
Korea
2
5
-3.06
9.36
-0.06
0.0036
Slovenia
2
3
-3.06
9.36
-2.06
4.24
Finlad
2
2
-3.06
9.36
-3.06
9.36
France
5
7
-0.06
0.0036
1.94
3.06
Germany
12
10
6.94
48.10
4.94
24.40
2
1.94
3.76
-3.06
9.36
Switzerland 7
= 76
=76
MEAN:
5.06
MEAN:
5.06
=163.72
=141.62
Step 2:
SD2 = Σ ((x1 - x̄1)) 2
n–1
SD2 = Σ (y1 - ȳ1) 2
n–1
= 163. 72
15 – 1
= 141.62
15 – 1
= 163.72
14
= 141.62
14
= 11.69
= 10.12
Step 3:
t = x̄1 - ȳ1
SD12 + SD22
n1
n2
= 5.06 – 5.06
11.69 + 10.12
15
15
= 1.45 computed value
Step 4:
DF = N – 1
DF = 15 – 1
DF = 14
TV 0.01 – 2.977
TV 0.05 – 2.145
Conclusion: After a careful computation of t-test, I arrived at the value of 1.45.
Based on the Tabulator Value (TV) Law: TV 0.01=2977 and TV 0.05=2.145. So
my Computed Value (CV) is less than the Tabulator Value (TV). This mean that
there is no significant difference between the no. of gold medals and silver medals
obtained by the 15 countries that has participated the 2022 Beijing China Olympic.