Question

using the data below, eve created a conditional relative frequency table by column and bob created a conditional relative frequency table by row. which statements are true? check all that apply. based on both tables, there is no association between gender and enjoying dancing. eves table shows that those who enjoy dancing are likely girls. bobs table shows that boys are likely to not enjoy dancing. the two tables will be identical since boys and girls have the same total number. the percentage of someone being a girl, given that the person enjoys dancing is lower than the percentage that someone enjoys dancing, given that the person is a girl.

	enjoys dancing	does not enjoy dancing	total
girls	40	10	50
total	60	40	100

Explanation:

Step1: Calculate conditional - relative frequencies

For Eve's column - based table:
The conditional relative frequency of being a boy given enjoying dancing is $\frac{20}{60}=\frac{1}{3}\approx0.33$, and of being a girl given enjoying dancing is $\frac{40}{60}=\frac{2}{3}\approx0.67$. So those who enjoy dancing are likely girls.
For Bob's row - based table:
The conditional relative frequency of not enjoying dancing for boys is $\frac{30}{50} = 0.6$, so boys are likely to not enjoy dancing.

Step2: Analyze association

The conditional relative frequencies show that there is an association between gender and enjoying dancing.
The two tables are not identical as they are calculated differently (column - based and row - based).
The percentage of someone being a girl, given that the person enjoys dancing is $\frac{40}{60}\approx0.67$. The percentage that someone enjoys dancing, given that the person is a girl is $\frac{40}{50}=0.8$. So the percentage of someone being a girl, given that the person enjoys dancing is lower than the percentage that someone enjoys dancing, given that the person is a girl.

Answer:

Eve's table shows that those who enjoy dancing are likely girls.
Bob's table shows that boys are likely to not enjoy dancing.
The percentage of someone being a girl, given that the person enjoys dancing is lower than the percentage that someone enjoys dancing, given that the person is a girl.