To determine an association between the categories in the given conditional relative frequency table, we can analyze the similarities between the values.
Here is the filled table with hypothetical values:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & Daisy & Rose & Total \\
\hline Red & 0.3 & 0.4 & 0.7 \\
\hline Yellow & 0.5 & 0.4 & 0.9 \\
\hline White & 0.2 & 0.3 & 0.5 \\
\hline Total & 1.0 & 1.0 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Now let’s explore the options for indicating an association between the categorical variables.
1. The value of [tex]$G$[/tex] is similar to the value of [tex]$H$[/tex].
- [tex]\( G = 0.2 \)[/tex]
- [tex]\( H = 0.3 \)[/tex]
- The difference [tex]\( |G - H| = |0.2 - 0.3| = 0.1 \)[/tex]
2. The value of [tex]$B$[/tex] is similar to the value of [tex]$E$[/tex].
- [tex]\( B = 0.4 \)[/tex]
- [tex]\( E = 0.4 \)[/tex]
- The difference [tex]\( |B - E| = |0.4 - 0.4| = 0 \)[/tex]
3. The value of [tex]$G$[/tex] is not similar to the value of [tex]$H$[/tex].
- This suggests a large difference, but as calculated above, [tex]\( |G - H| = 0.1 \)[/tex], which is a small difference.
4. The value of [tex]$B$[/tex] is not similar to the value of [tex]$E$[/tex].
- This suggests a large difference, but as calculated above, [tex]\( |B - E| = 0 \)[/tex], which is identical.
Given these comparisons, the most likely indicator of an association between the categorical variables is if the values are similar. The closest values in our table are [tex]$B$[/tex] and [tex]$E$[/tex] with [tex]\( |B - E| = 0 \)[/tex], which is exactly the same.
Therefore, the correct answer is:
The value of [tex]\( B \)[/tex] is similar to the value of [tex]\( E \)[/tex].
