To determine the association between categorical variables, we need to examine the conditional relative frequencies to see how similarly or differently males and females prefer cooking particular meals.
Here is the given table:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{ Favorite Meal to Cook } \\
\cline { 2 - 5 } & Breakfast & Lunch & Dinner & Total \\
\hline Male & A & B & C & D \\
\hline Female & E & F & G & H \\
\hline Total & 1.0 & 1.0 & 1.0 & 1.0 \\
\hline
\end{tabular}
\][/tex]
To indicate an association between gender and favorite meal to cook, there should be a noticeable difference between the values when comparing these categories.
Let's evaluate each option:
1. The value of [tex]\( A \)[/tex] is similar to the value of [tex]\( B \)[/tex]:
- This comparison checks for similarity within the male category (breakfast vs lunch). Similar values here would not necessarily indicate an association between gender and meal preference because it only looks at one gender’s preferences.
2. The value of [tex]\( A \)[/tex] is similar to the value of [tex]\( E \)[/tex]:
- This comparison looks at the proportion of males who prefer breakfast versus the proportion of females who prefer breakfast. Similar values would indicate a lack of association because both genders prefer breakfast equally.
3. The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( C \)[/tex]:
- This compares the preference within the male category (lunch vs dinner). Differences between these values show variation in meal preferences by males, but do not necessarily indicate an association between gender and meal preference.
4. The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( F \)[/tex]:
- This checks the proportion of males who prefer lunch vs the proportion of females who prefer lunch. A significant difference here would indicate that gender is associated with meal preference since males and females have different preferences for the same meal category.
The most likely indicator of an association between gender and favorite meal to cook is:
The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( F \)[/tex].
This is because it shows a comparison between males' and females' preferences for lunch, suggesting that gender may play a role in determining which meal individuals prefer to cook.
