GOALKEEPER JUMP Left Center Right Kick to Left 52 5 45 Kick to Center 39 12...

GOALKEEPER JUMP

	Left	Center	Right
Kick to Left	52	5	45
Kick to Center	39	12	35
Kick to Right	50	5	59

In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from 302 kicks during games among top teams. In the table, jump direction indicates which way the goalkeeper jumped, where the kick direction is from the perspective of the goalkeeper. Use a 0.01 significance level to test the claim that the direction of the kick is independent of the direction of the goalkeeper jump. Do the results support the theory that because the kicks are so fast, goalkeepers have no time to react, so the directions of their jumps are independent of the directions of the kicks? (round to 3 decimals as needed)

Solutions

Expert Solution

Alpha, = 0.01

Null hypothesis
H0: direction of the kick is independent of the direction of the goalkeeper jump

Alternative hypothesis
H1: direction of the kick is not independent of the direction of the goalkeeper jump

observed frequencies,f0:

	Left	Center	Right	Total
Kick to Left	52	5	45	102
Kick to Center	39	12	35	86
Kick to Right	50	5	59	114
Total	141	22	139	302

expected frequencies,fe:
fe = (row total * column total) / total
for example:
fe1 = 102*141/302 = 47.6225
fe5 = 86*22/302 = 6.265

	Right	Center	Left
Kick to Right	47.6225	7.4305	46.947
Kick to Center	40.1523	6.265	39.5828
Kick to Left	53.225	8.305	52.4702

f_0	f_e	(f_0-f_e)^2	(f0-fe)^2 / fe
52	47.6225	19.1625	0.4024
5	7.4305	5.9073	0.7950
45	46.947	3.7908	0.0807
39	40.1523	1.3278	0.0331
12	6.265	32.8902	5.2498
35	39.5828	21.0020	0.5306
50	53.225	10.4006	0.1954
5	8.305	10.9230	1.3152
59	52.4702	42.6383	0.8126
		Sum	9.4148

test statistic,X^2 = 9.4148

degree of freedom = (number of rows - 1) * (number of columns - 1) [not including total]
df = (3-1)*(3-1) = 4

P_value = 0.0007
Since P_value < 0.05, hence reject H0.

We can conclude that the direction of the kick is not independent of the direction of the goalkeeper jump.

orchestra answered 2 years ago

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