Explanation:
If two variables x and y are independent, then:
P(x and y) = P(x) P(y)
Or, in terms of conditional probability:
P(x given y) = P(x)
From part 3, 27.3% of the students are sophomores, 57.8% are juniors, and 14.8% are seniors.
From part 4, 31.6% of procrastinators are sophomores, 53.6% are juniors, and 14.8% are seniors.
Since the percent of procrastinators that are sophmores is not the same as the percent of students that are sophmores, the variables are not independent, which means there is a relationship between academic level and whether students procrastinate.