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

If there is no association, the conditional - relative frequencies would be similar across different categories. Calculate conditional - relative frequencies. For Eve's column - based table, the conditional relative frequency of being a girl given enjoying dancing is $\frac{40}{60}=\frac{2}{3}\approx0.67$, and for boys given enjoying dancing is $\frac{20}{60}=\frac{1}{3}\approx0.33$. So, there is an association between gender and enjoying dancing, and the first statement is false.

Step2: Check Eve's table

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

Step3: Check Bob's table

In Bob's row - based conditional relative frequency table, the proportion of boys 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: Compare the two tables

Eve's table is column - based and Bob's is row - based. They will not be identical as they calculate conditional relative frequencies in different ways, so the fourth statement is false.

Step5: Calculate conditional percentages

The percentage of someone being a girl, given that the person enjoys dancing is $\frac{40}{60}\times100\%\approx66.7\%$. The percentage that someone enjoys dancing, given that the person is a girl is $\frac{40}{50}\times100\% = 80\%$. So, the fifth statement is true.

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.