To determine an association between categorical variables, we need to look for variations in the distribution of frequencies across the categories.
The given conditional relative frequency table shows the distribution of favorite meals to cook by gender:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
& \text{Breakfast} & \text{Lunch} & \text{Dinner} & \text{Total} \\
\hline
\text{Male} & A & B & C & D \\
\hline
\text{Female} & E & F & G & H \\
\hline
\text{Total} & 1.0 & 1.0 & 1.0 & 1.0 \\
\hline
\end{array}
\][/tex]
Each column sums to 1.0, indicating these are relative frequencies.
To find an association between the categorical variables (gender and favorite meal to cook), we look for differences in the preferences between males and females.
### Explanation for Each Option:
1. The value of [tex]$A$[/tex] is similar to the value of [tex]$B$[/tex].
- This compares male preferences for breakfast (A) with male preferences for lunch (B).
- This does not reveal any association between gender and meal preference.
2. The value of [tex]$A$[/tex] is similar to the value of [tex]$E$[/tex].
- This compares male preferences for breakfast (A) with female preferences for breakfast (E).
- If these values are similar, it would suggest no association for breakfast preference between genders.
- If dissimilar, it could indicate an association.
3. The value of [tex]$B$[/tex] is not similar to the value of [tex]$C$[/tex].
- This compares male preferences for lunch (B) with male preferences for dinner (C).
- This does not indicate an association between gender and meal preference, only within male preferences.
4. The value of [tex]$B$[/tex] is not similar to the value of [tex]$F$[/tex].
- This compares male preferences for lunch (B) with female preferences for lunch (F).
- If these values are not similar, it suggests a difference in lunch preferences for males and females, indicating a possible association between gender and lunch preferences.
### Conclusion:
The correct choice is:
The value of [tex]$B$[/tex] is not similar to the value of [tex]$F$[/tex].
This option compares the distributions between genders for the same meal category (lunch) and differences here would most likely indicate an association between the categorical variables (gender and favorite meal to cook).
