Question

shooter
kick left kick right total
goalie move left 80 132 212
move right 85 75 160
total 165 207 372
which of the following indicates an association between the shooters choice of direction and the goalies 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 shooters direction.
e for the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooters direction.

Explanation:

Step1: Recall the concept of association

Association in a two - way table means that the relative frequencies for one variable depend on the value of the other variable.

Step2: Analyze each option

• Option A: Marginal relative frequencies being equal has no relation to association between the two variables.
• Option B: Marginal relative frequencies not being equal also does not imply association.
• Option C: Row totals not being equal is not an indicator of association.
• Option D: If the relative frequency of a direction for the goalie is equal to the relative frequency conditioned on the shooter's direction, there is no association.
• Option E: If for the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction, it indicates an association between the shooter's choice of direction and the goalie's choice of direction.

Answer:

E. For the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction.