Question

comparing relative frequency tables
using the data below, eve created a conditional relative frequency table by column and bob created a conditional relative frequency table by row.

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

which statements are true? check all that apply.

• ☐ based on both tables, there is no association between gender and enjoying dancing.
• ☐ 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 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.

Explanation:

To solve this, we analyze each statement using the given data:

1. "Based on both tables, there is no association between gender and enjoying dancing."

• For Eve (column - conditional):
• % of boys who enjoy dancing: $\frac{20}{60} \approx 33.3\%$; % of girls who enjoy dancing: $\frac{40}{60} \approx 66.7\%$.
• For Bob (row - conditional):
• % of boys who enjoy dancing: $\frac{20}{50} = 40\%$; % of boys who don’t: $\frac{30}{50} = 60\%$.
• % of girls who enjoy dancing: $\frac{40}{50} = 80\%$; % of girls who don’t: $\frac{10}{50} = 20\%$.
• Since these percentages differ, there is an association. So this statement is false.

2. "Eve’s table shows that those who enjoy dancing are likely girls."

• Eve’s table (column - conditional) for “Enjoys Dancing”:
• % of boys: $\frac{20}{60} \approx 33.3\%$; % of girls: $\frac{40}{60} \approx 66.7\%$.
• Since 66.7% (girls) > 33.3% (boys), those who enjoy dancing are more likely girls. This statement is true.

3. "Bob’s table shows that boys are likely to not enjoy dancing."

• Bob’s table (row - conditional) for “Boys”:
• % who enjoy dancing: $\frac{20}{50} = 40\%$; % who don’t: $\frac{30}{50} = 60\%$.
• Since 60% (don’t enjoy) > 40% (enjoy), boys are likely to not enjoy dancing. This statement is true.

4. "The two tables will be identical since boys and girls have the same total number."

• Eve’s table (column - conditional) focuses on column totals (60, 40), while Bob’s (row - conditional) focuses on row totals (50, 50).
• For example, Eve’s “Enjoys Dancing” column: $\frac{20}{60}, \frac{40}{60}$; Bob’s “Boys” row: $\frac{20}{50}, \frac{30}{50}$. These are different. So the tables are not identical. This statement is false.

5. "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."

• Let’s calculate both:
• “Girl, given enjoys dancing” (Eve’s table): $\frac{40}{60} \approx 66.7\%$.
• “Enjoys dancing, given girl” (Bob’s table): $\frac{40}{50} = 80\%$.
• $66.7\% < 80\%$, so this statement is true.

Answer:

The true statements are:

• 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.

(In boxed form for the selected options, assuming the options are labeled as follows:
A. Based on both tables...
B. Eve’s table shows...
C. Bob’s table shows...
D. The two tables will...
E. The percentage of someone...

Then the answer is: B. Eve’s table shows that those who enjoy dancing are likely girls., C. Bob’s table shows that boys are likely to not enjoy dancing., E. 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.)