Question

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

287287

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

0.050.05

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	5959	11	3737
Kick to Center	4141	99	3434
Kick to Right	4040	66	6060

Determine the null and alternative hypotheses.

A.

Upper H 0H0​:

Goalkeepers jump in the direction of the kick.

Upper H 1H1​:

Goalkeepers do not jump in the direction of the kick.

B.

Upper H 0H0​:

Goalkeepers do not jump in the direction of the kick.

Upper H 1H1​:

Goalkeepers jump in the direction of the kick.

C.

Upper H 0H0​:

Jump direction is dependent on kick direction.

Upper H 1H1​:

Jump direction is independent of kick direction.

D.

Upper H 0H0​:

Jump direction is independent of kick direction.

Upper H 1H1​:

Jump direction is dependent on kick direction.

Determine the test statistic.

chi squaredχ2equals=nothing

​(Round to three decimal places as​ needed.)

Determine the​ P-value of the test statistic.

​P-valueequals=nothing

​(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

▼

sufficient

insufficient

evidence to warrant rejection of the claim that the direction of the kick is independent of the direction of the goalkeeper jump. The results

▼

do not support

support

the theory that because the kicks are so​ fast, goalkeepers have no time to react.

Answer 1

The statistical software output for this problem is:

Contingency table results:

Rows: var1
Columns: None

	Left	Center	Right	Total
Kick to left	59	1	37	97
Kick to center	41	9	34	84
Kick to right	40	6	60	106
Total	140	16	131	287

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	4	17.585311	0.0015

Hence,

Hypotheses: Option D is correct.

Test statistic = 17.585

P-value = 0.0015

Conclusion: ​​​​​​ Sufficient; Do not support