Mary (a woman) is choosing between restaurants A and B to take her friend, John (a man), out for dinner. Restaurant A has an average rating of 4.1 and restaurant B of 4.3. But looking at ratings by gender, among men, restaurant A has a rating of 4.0 and restaurant B of 3.8. Among women, restaurant A has a rating of 4.6 and restaurant B of 4.4. It seems that men and women separately prefer restaurant A but together they prefer restaurant B! Draw a Paik-Agresti diagram conditioning on the gender with restaurant on the horizontal axis and average ratings on the vertical axis to explain how this apparent contradiction could arise. Draw a causal graph describing the relationships among the three variables: restaurant, gender and ratings. Assuming that there are no other significant factors related to restaurant ratings, what kind of variable is gender in this context? Which restaurant should Mary choose? Why