To determine the association between the categorical variables (gender and a person's favorite meal to cook) using the conditional relative frequency table, follow these steps:
1. Identify the Variables and Their Categories:
- The categorical variables in question are "Gender" and "Favorite Meal to Cook."
- The categories for Favorite Meal to Cook are "Breakfast," "Lunch," and "Dinner."
- The categories for Gender are "Male" and "Female."
2. Understand the Structure of the Table:
- The table presents the relative frequencies of the favorite meal to cook by gender.
- Each column sums to 1.0 (indicating the relative frequencies within each meal type).
3. Evaluate Each Statement:
- The value of [tex]\( A \)[/tex] is similar to the value of [tex]\( B \)[/tex]: This would indicate that the preference for Breakfast and Lunch among males is similar.
- The value of [tex]\( A \)[/tex] is similar to the value of [tex]\( E \)[/tex]: This would indicate that the preference for Breakfast between males and females is similar.
- The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( C \)[/tex]: This would indicate that the preference for Lunch and Dinner among males is different.
- The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( F \)[/tex]: This would suggest that the preference for Lunch between males and females is different.
4. Determine the Most Likely Indicator of Association:
- An association between the categorical variables would be indicated by a difference in the distribution of preferences between the two gender groups.
- The statement "The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( F \)[/tex]" would indicate that males and females have different relative frequencies for choosing Lunch as their favorite meal to cook, suggesting an association between gender and the likelihood of cooking lunch.
Therefore, the most likely indication of an association between gender and favorite meal to cook is if:
The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( F \)[/tex].
Thus, the correct answer is:
4. The value of [tex]\( B \)[/tex] is not similar to the value of [tex]\( F \)[/tex].
