Siloni computed in a two-way table the relative frequencies of boys’ and girls’ participation in school sports at her school.

Question

School Sports Participation by Gender


Fall
Spring
Boys
37%
57%
Girls
63%
43%

Which statement best describes the relationship between the two variables?
There is an association because the relative frequencies by column are different.
There is an association because the relative frequencies by row are different.
There is no association because the relative frequencies by column are different.
There is no association because the relative frequencies by row are different.

Answer 1

To determine the relationship between the two variables (gender and season of sports participation), we can analyze the relative frequencies given in the table.

From the data:

• In the Fall:

  • Boys: 37%
  • Girls: 63%

• In the Spring:

  • Boys: 57%
  • Girls: 43%

Now, look at the relative frequencies by column (Fall and Spring):

• The percentage of boys participating is different in Fall (37%) compared to Spring (57%).
• The percentage of girls participating is also different in Fall (63%) compared to Spring (43%).

Now, let's consider the rows:

• The boys' participation percentages are 37% in Fall and 57% in Spring.
• The girls' participation percentages are 63% in Fall and 43% in Spring.

Since the frequencies for both boys and girls change across the seasons, we can conclude that there is an association based on the column (the season).

Therefore, the best statement that describes the relationship is: There is an association because the relative frequencies by column are different.