3 In soccer serious fouls result in a penalty kick with one

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In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The accompanying table summarizes results from 285 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 0.05 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?

_ Jump_Left Jump_Center Jump_Right
Kick_Left 51 1 38
Kick_Center 36 15 33
Kick_Right 44 8 59

What is The Test Statistic_________(round to 4 decimal places)

What is the P value (Round to 4 decimal places)

Whats is the Null hYpoothesis:

What is the research hypothesis:

Reject or fail to reject he null hypothesis_______ there is or is not suifficent evidence to suppport the claiim________because P is> or <________

Solution

alpha,a = 0.05

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

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

observed frequencies,f0:

expected frequencies,fe:
fe = (row total * column total) / total
for example:
fe1 = 90*131/285 = 41.368
fe5 = 84*24/285 = 7.074

.

test statistic,X^2 = 20.52

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

P_value = 0.0004
Since P_value < 0.05, hence reject H0