Question

jordan computed in a two-way table the relative frequencies of the weather on practice days and game days during his football season.

weather during football
\

$$\begin{tabular}{|c|c|c|} \\hline & raining & not raining \\\\ \\hline practices & 23\\% & 77\\% \\\\ \\hline games & 13\\% & 87\\% \\\\ \\hline \\end{tabular}$$

which statement best describes the relationship between the two variables?
there appears to be an association because the relative frequencies by column are different.
there appears to be an association because the relative frequencies by row are different.
there does not appear to be an association because the relative frequencies by column are different.
there does not appear to be an association because the relative frequencies by row are different.

Explanation:

Analyze the row relative frequencies

The table displays row relative frequencies because each row sums to \(100\%\):

• Practices: \(23\% + 77\% = 100\%\)
• Games: \(13\% + 87\% = 100\%\)

Determine association

An association exists between two categorical variables if the conditional relative frequencies (by row or by column) are different. Here, the relative frequencies by row are different (\(23\%\) vs \(13\%\) and \(77\%\) vs \(87\%\)), which indicates an association.

Match with the correct option

The statement that best describes this is: "There appears to be an association because the relative frequencies by row are different."

Answer:

• There appears to be an association because the relative frequencies by column are different.
• There appears to be an association because the relative frequencies by row are different. (Correct answer)
• There does not appear to be an association because the relative frequencies by column are different.
• There does not appear to be an association because the relative frequencies by row are different.