A penalty kick in soccer involves two players from different teams, the shooter and the goalie. During the penalty kick the shooter will try to score a goal by kicking a soccer ball to the left or right of the goal area. To prevent the shooter from scoring a goal, the goalie will move to the left or right of the goal area. The following table summarizes the directions taken by the shooter and the goalie for 372 penalty kicks.
Which of the following indicates an association between the shooter's choice of direction and the goalie's choice of direction?

A The marginal relative frequencies for the shooter and the goalie are equal.
B The marginal relative frequencies for the shooter and the goalie are not equal.
C The row totals are not equal.
D For the goalie, the relative frequency of a direction is equal to the relative frequency conditioned on the shooter's direction.
E For the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.

Question

20-12-2022
Mathematics

Answered

A penalty kick in soccer involves two players from different teams, the shooter and the goalie. During the penalty kick the shooter will try to score a goal by kicking a soccer ball to the left or right of the goal area. To prevent the shooter from scoring a goal, the goalie will move to the left or right of the goal area. The following table summarizes the directions taken by the shooter and the goalie for 372 penalty kicks.
Which of the following indicates an association between the shooter's choice of direction and the goalie's choice of direction?

A The marginal relative frequencies for the shooter and the goalie are equal.
B The marginal relative frequencies for the shooter and the goalie are not equal.
C The row totals are not equal.
D For the goalie, the relative frequency of a direction is equal to the relative frequency conditioned on the shooter's direction.
E For the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.

Answer :

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-24T03:48:06-05:00

E The relative frequency of a direction for the goalie is not the same as the relative frequency adjusted for the shooter's direction.

A is incorrect because the marginal relative frequencies for the shooter and the goalie are not equal.

B is incorrect because this does not indicate an association between the shooter's choice of direction and the goalie's choice of direction.

C is incorrect because this does not indicate an association between the shooter's choice of direction and the goalie's choice of direction.

D is incorrect because for the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.

E is correct because it indicates that there is an association between the shooter's choice of direction and the goalie's choice of direction. This is because the relative frequency of a direction for the goalie is not equal to the relative frequency conditioned on the shooter's direction.

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