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: Analyze association

Calculate conditional - relative frequencies. For Eve's column - based table and Bob's row - based table, we can see patterns. The proportion of girls who enjoy dancing ($\frac{40}{60}=\frac{2}{3}$) and boys who enjoy dancing ($\frac{20}{60}=\frac{1}{3}$) shows an association between gender and enjoying dancing, so the first statement is false.

Step2: Analyze Eve's table

In Eve's column - based conditional relative frequency table, among those who enjoy dancing, the proportion of girls is $\frac{40}{60}\approx0.67$, so Eve's table shows that those who enjoy dancing are likely girls, and the second statement is true.

Step3: Analyze Bob's table

In Bob's row - based conditional relative frequency table, for boys, the proportion of those who do not enjoy dancing is $\frac{30}{50} = 0.6$, so Bob's table shows that boys are likely to not enjoy dancing, and the third statement is true.

Step4: Analyze table identity

Eve's table is column - based and Bob's table is row - based. Their calculations are different, so the two tables are not identical, and the fourth statement is false.

Step5: Calculate conditional probabilities

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 fifth statement is false.

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.