An association implies that a variable affects other.
See solution.
Practice makes perfect
Having an association between two characteristics means that there is a pattern between two variables, so that the conditional relative frequencies, or conditional probabilities, somewhat follow a predictable behavior or rule.
Example
A survey asks asks a group of 40 students their favorite fruit, obtaining the results shown below. From this group, we know that 18 students were girls.
Apple
Banana
Orange
Of the 18 students who preferred apples, 10 are girls. 1018≈ 0.556 = 55.6 %
Of the 20 students who preferred bananas, 5 are girls. 520= 0.25 = 25 %
Of the 7 students who preferred oranges, 3 are girls. 37≈ 0.428 = 42.8 %
Let's calculate the percentage of students who are girls.
Now we can compare the conditional relative frequencies to the percent of girls surveyed. If the preferred fruit was not influenced by the gende,r we would expect the distribution of gender among the preferred fruits to be roughly equal to the distribution of the whole group. Let's analyze the results.
Results for apples
Since 55.6 %>40 %, we can conclude that girls are more likely to prefer apples.
Results for bananas
Since 25 %<40 %, we can conclude that girls are less likely to prefer bananas.
Results for oranges
Since 43.7 % ~ 40 %, we can conclude that gender does not have a big influence in the students that prefer oranges.
