Question

The Dallas Mavericks won the NBA championship in the 2010–2011 season. The two-way table displays the relationship between the outcome of each game in the regular season and whether the Mavericks scored at least 100 points.

Which of the following is the best evidence that there is an association between the outcome of a game and whether or not the Mavericks scored at least 100 points?

(a) The Mavericks won 57 games and lost only 25 games.

(b) The Mavericks scored at least 100 points in 47 games and fewer than 100 points in only 35 games.

(c) The Mavericks won 43 games when scoring at least 100 points and only 14 games when scoring fewer than 100 points.

(d) The Mavericks won a higher proportion of games when scoring at least 100 points (43/47) than when they scored fewer than 100 points (14/35).

(e) The combination of scoring 100 or more points and winning the game occurred more often (43 times) than any other combination of outcomes.

Short answer

Option (d) "The Mavericks won a higher proportion of games when scoring at least 100 points (43/47) than when they scored fewer than 100 points (14/35). " is the correct option.

Step-by-step solution

Step 1. Given information.

The given table is:

Step 2. Explanation for the correct option.

The answer (a) just tells us how many games the Mavericks have won and how many games they have lost.

The answer (b) tells us how many games the Mavericks have scored more than 100 points in and how many games they have scored fewer than 100 points in.

The solution (c) only tells us about games that the Mavericks won.

The information on scoring using the population proportion can be found in answer (d).

We can compare these two proportions to see if there is a link between them. Given the value of $\frac{43}{47}=0.91$, we can deduce that if the Mavericks score more than 100 points, they have a 91 percent chance of winning.

Since $\frac{14}{35}=0.4$, we can deduce that if the Mavericks score less than 100 points, they have a 10% chance of winning.

The answer (e) simply tells us about the highest-scoring person.

Therefore, from the above explanation we can say that there is a link between the outcome of each game in the regular season and whether the Mavericks scored at least 100 points according to option (d).

As a result Option (d) is the correct option.