GOALKEEPER JUMP Left Center Ri

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 onekicker and one defending goalkeeper. The accompanying tablesummarizes results from 302 kicks during games among top teams. Inthe​ table, jump direction indicates which way the goalkeeper​jumped, where the kick direction is from the perspective of thegoalkeeper. Use a 0.01 significance level to test the claim thatthe direction of the kick is independent of the direction of thegoalkeeper jump. Do the results support the theory that because thekicks are so​ fast, goalkeepers have no time to​ react, so thedirections of their jumps are independent of the directions of the​kicks? (round to 3 decimals as needed)

Answer:

Alpha, = 0.01

Null hypothesisH0: direction of the kick is independent of the direction of thegoalkeeper jump

Alternative hypothesisH1: direction of the kick is not independent of the direction ofthe 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) / totalfor example:fe1 = 102*141/302 = 47.6225fe5 = 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 = 0.0007Since P_value < 0.05, hence reject H0.

We can conclude that the direction of the kick is notindependent of the direction of the goalkeeper jump.


 
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