Problem 13BSC
In Exercise, test the given claim.
Soccer Strategy In soccer, serious fouls result in a penalty kick with one kicker and one defending goalkeeper. The table below summarizes results from 286 kicks during games among top teams (based on data from “Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks,” by BarEli et al., Journal of Economic Psychology, Vol. 28, No. 5). 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?

Goalkeeper Jump 



Left 
Center 
Right 
Kick to Left 
54 
1 
37 
Kick to Center 
41 
10 
31 
Kick to Right 
46 
7 
59 
Solution 13BSC
We are given a data set of results of jump direction and kick direction for a sample of 286 kicks. We have to test the claim that jump directions are independent of kick directions.
Step 1: To test the claim we need to fulfil certain assumptions.
1. We assume that the sample has been randomly selected because of the structure of the study.
2. The results are tabulated as frequencies.
3. The expected frequencies are more than five in every column.