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)

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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