1. The problem asks to identify two pairs of categorical variables: one pair that might be associated and one pair that might not be associated. 2. Let's define the pairs: - Associated variables: Gender (Male, Female) and Preference for a new product (Like, Dislike) - Not associated variables: Eye color (Blue, Brown) and Favorite fruit (Apple, Banana) 3. Create two-way tables with 100 total values each. Associated variables table: | Gender | Like | Dislike | Total | |--------|------|---------|-------| | Male | 30 | 20 | 50 | | Female | 40 | 10 | 50 | | Total | 70 | 30 | 100 | Not associated variables table: | Eye Color | Apple | Banana | Total | |-----------|-------|--------|-------| | Blue | 25 | 25 | 50 | | Brown | 25 | 25 | 50 | | Total | 50 | 50 | 100 | 4. Explanation: - For the associated variables, the distribution of preferences differs by gender: 60% of females like the product compared to 60% of males disliking it, indicating an association. - For the not associated variables, the distribution of favorite fruit is the same regardless of eye color, showing no association. Final answer: The first pair shows association because the preference depends on gender, while the second pair shows no association because the favorite fruit is independent of eye color.