Answer :
To solve this question, we need to understand what an association between categorical variables means. In the context of a conditional relative frequency table, an association is indicated when comparing the occurrences of categories in one variable (flower color) relative to another variable (type of flower) shows a relationship.
Here's the given table for reference:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Daisy & Rose & Total \\ \hline Red & A & B & C \\ \hline Yellow & D & E & F \\ \hline White & G & H & J \\ \hline Total & 1.0 & 1.0 & 10 \\ \hline \end{tabular} \][/tex]
Now, let's analyze the possible options to identify an association:
### Option A: The value of [tex]\( G \)[/tex] is similar to the value of [tex]\( H \)[/tex].
If [tex]\( G \)[/tex] is similar to [tex]\( H \)[/tex], it implies that the relative frequencies of white flowers for both daisies and roses are nearly the same. This suggests that the type of flower (daisy or rose) does not influence the likelihood of being a white flower, indicating no association between flower type and color.
### Option B: The value of [tex]\( B \)[/tex] is similar to the value of [tex]\( E \)[/tex].
If [tex]\( B \)[/tex] is similar to [tex]\( E \)[/tex], it means that the relative frequencies of red daisies and yellow roses are similar. This implies a potential association between the flower type (daisy or rose) and the colors red and yellow. In comparing the distribution of colors in both flower types, we see a commonality which suggests an association.
### Option C: The value of [tex]\( G \)[/tex] is not similar to the value of [tex]\( H \)[/tex].
If [tex]\( G \)[/tex] is not similar to [tex]\( H \)[/tex], it indicates differing relative frequencies for white flowers among daisies and roses. This would suggest that the flower type does affect the likelihood of being a white flower, hence indicating an association. However, we are looking for which option most strongly indicates this.
### Option D: The value of [tex]\( R \)[/tex] is not similar to the value of [tex]\( F \)[/tex].
This option uses undefined terms [tex]\( R \)[/tex] and [tex]\( F \)[/tex], making it unclear and irrelevant for identifying association from the given table.
Considering these, the most relevant comparison which suggests an association between the categorical variables is:
### Option B: The value of [tex]\( B \)[/tex] is similar to the value of [tex]\( E \)[/tex].
This option suggests that there is an observed pattern between the color distribution in the given flower types, and thus it is most likely to indicate an association between the categorical variables.
Therefore, the answer is [tex]\( \boxed{2} \)[/tex].
Here's the given table for reference:
[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Daisy & Rose & Total \\ \hline Red & A & B & C \\ \hline Yellow & D & E & F \\ \hline White & G & H & J \\ \hline Total & 1.0 & 1.0 & 10 \\ \hline \end{tabular} \][/tex]
Now, let's analyze the possible options to identify an association:
### Option A: The value of [tex]\( G \)[/tex] is similar to the value of [tex]\( H \)[/tex].
If [tex]\( G \)[/tex] is similar to [tex]\( H \)[/tex], it implies that the relative frequencies of white flowers for both daisies and roses are nearly the same. This suggests that the type of flower (daisy or rose) does not influence the likelihood of being a white flower, indicating no association between flower type and color.
### Option B: The value of [tex]\( B \)[/tex] is similar to the value of [tex]\( E \)[/tex].
If [tex]\( B \)[/tex] is similar to [tex]\( E \)[/tex], it means that the relative frequencies of red daisies and yellow roses are similar. This implies a potential association between the flower type (daisy or rose) and the colors red and yellow. In comparing the distribution of colors in both flower types, we see a commonality which suggests an association.
### Option C: The value of [tex]\( G \)[/tex] is not similar to the value of [tex]\( H \)[/tex].
If [tex]\( G \)[/tex] is not similar to [tex]\( H \)[/tex], it indicates differing relative frequencies for white flowers among daisies and roses. This would suggest that the flower type does affect the likelihood of being a white flower, hence indicating an association. However, we are looking for which option most strongly indicates this.
### Option D: The value of [tex]\( R \)[/tex] is not similar to the value of [tex]\( F \)[/tex].
This option uses undefined terms [tex]\( R \)[/tex] and [tex]\( F \)[/tex], making it unclear and irrelevant for identifying association from the given table.
Considering these, the most relevant comparison which suggests an association between the categorical variables is:
### Option B: The value of [tex]\( B \)[/tex] is similar to the value of [tex]\( E \)[/tex].
This option suggests that there is an observed pattern between the color distribution in the given flower types, and thus it is most likely to indicate an association between the categorical variables.
Therefore, the answer is [tex]\( \boxed{2} \)[/tex].
