A service station near an interstate highway sells three grades of gasoline: regular, plus, and premium. During the last week, the manager counted the number of cars that purchased these types of gasoline. He kept the counts separate for weekdays and the weekend. The data table has two categorical variables. One distinguishes weekdays from weekends, and the other indicates the type of gas (regular, plus, or premium).
(a) Find the contingency table defined by the day of the week and the type of gas. Include the marginal distributions.
(b) Find the conditional distribution of purchase type for weekday purchases.
(c) Find the conditional distribution of premium purchases during the week and weekend.
(d) Does the fact that your answers to parts (b) and
(c) are different indicate association?
(e) The owner of the station would like to develop better ties to customers who buy premium gas. (The owner expects these customers to be more affluent and likely to purchase other services from the station.) If the owner wants to meet more of these customers, when should the owner be around the station: on weekdays or weekends?