### Penalty Kick Statistical AnalysisIn 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 0.01 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?---#### Determine the Null and Alternative Hypotheses**Options:**- **A.** - \(H_0\): Jump direction is independent of kick direction. - \(H_1\): Jump direction is dependent on kick direction.- **B.** - \(H_0\): Goalkeepers jump in the direction of the kick. - \(H_1\): Goalkeepers do not jump in the direction of the kick.- **C.** - \(H_0\): Goalkeepers do not jump in the direction of the kick. - \(H_1\): Goalkeepers jump in the direction of the kick.- **D.** - \(H_0\): Jump direction is dependent on kick direction. - \(H_1\): Jump direction is independent of kick direction.#### Determine the Test StatisticUse the formula for the chi-square test statistic:\[\chi^2 = \boxed{} \quad \text{(Round to three decimal places as needed.)}\]#### Determine the P-value of the Test Statistic\[\text{P-value} = \boxed{} \quad \text{(Round to four decimal places as needed.)}\]#### Evaluation of ResultsDo 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?There is \boxed{} evidence to warrant rejection of the claim that the direction of the kick is independent of the direction of the goalkeeper jump. The results \boxed{} the theory that because the kicks are so fast, goalkeepers have no time to react.---#### Data Table: Penalty Kick DataThe data from the study is summarized in the

It is needed to test the claim that whether the direction of the kick is independent of the…

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 0.01 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? Click the icon to view the penalty kick data. Determine the null and alternative hypotheses. X Pentalty Kick Data O A. Ho: Jump direction is independent of kick direction. H₁: Jump direction is dependent on kick direction. OB. Ho: Goalkeepers jump in the direction of the kick. H₁: Goalkeepers do not jump in the direction of the kick. Goalkeeper Jump Left Center Right 4 52 37 OC. Ho: Goalkeepers do not jump in the direction of the kick. H₁: Goalkeepers jump in the direction of the kick. Kick to Left Kick to Center Kick to Right 39 11 32 45 9 56 O D. Ho: Jump direction is dependent on kick direction. H₁: Jump direction is independent of kick direction. Determine the test statistic. Print Done x² = (Round to three decimal places as needed.) Determine the P-value of the test statistic. P-value = (Round to four decimal places as needed.) 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? There is evidence to warrant rejection of the claim that the direction of the kick is independent of the direction of the goalkeeper jump. The results the theory that because the kicks are so fast, goalkeepers have no time to react.

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS