To determine which condition most likely indicates an association between the categorical variables (in this case, gender and favorite meal to cook), let's carefully review each statement:
1. The value of [tex]\(A\)[/tex] is similar to the value of [tex]\(B\)[/tex].
2. The value of [tex]\(A\)[/tex] is similar to the value of [tex]\(E\)[/tex].
3. The value of [tex]\(B\)[/tex] is not similar to the value of [tex]\(C\)[/tex].
4. The value of [tex]\(B\)[/tex] is not similar to the value of [tex]\(F\)[/tex].
We evaluate these conditions with the given results:
- [tex]\(\text{Condition 1: } A = B \rightarrow \text{False}\)[/tex]
- [tex]\(\text{Condition 2: } A = E \rightarrow \text{True}\)[/tex]
- [tex]\(\text{Condition 3: } B \neq C \rightarrow \text{True}\)[/tex]
- [tex]\(\text{Condition 4: } B \neq F \rightarrow \text{True}\)[/tex]
Explanation of each condition:
1. Condition 1: [tex]\(A = B\)[/tex]
This evaluates to False, meaning [tex]\(A\)[/tex] is not similar to [tex]\(B\)[/tex], hence no association is suggested here.
2. Condition 2: [tex]\(A = E\)[/tex]
This evaluates to True, indicating that [tex]\(A\)[/tex] is similar to [tex]\(E\)[/tex]. This similarity suggests that there might be an association between the categorical variables (gender and the favorite meal to cook is the same for both genders for Breakfast).
3. Condition 3: [tex]\(B \neq C\)[/tex]
This is True, suggesting that values for Lunch (B) and Dinner (C) are not similar, which also indicates a potential association between gender and favorite meal to cook because different values might imply different meal preferences for one of the genders.
4. Condition 4: [tex]\(B \neq F\)[/tex]
This is True, indicating that the value for Lunch (B) and Lunch for the other gender (F) are not similar, which again supports the indication of an association.
So based on the evaluation:
- Condition 2: [tex]\(A = E\)[/tex], Condition 3: [tex]\(B \neq C\)[/tex], and Condition 4: [tex]\(B \neq F\)[/tex] are all likely to indicate an association between the categorical variables.
Given that the true conditions indicating an association are:
- [tex]\(A = E\)[/tex] (True)
- [tex]\(B \neq C\)[/tex] (True)
- [tex]\(B \neq F\)[/tex] (True)
We can confirm that choosing any of these statements suggests an association between the variables.
