1. C HAPTER 5: A SSOCIATION BETWEEN C ATEGORICAL V ARIABLES H OMEWORK #4

2. C HAPTER 5 P ROBLEM 39 Gasoline sales 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).

3. C HAPTER 5 P ROBLEM 39( A ) Find the contingency table defined by the day of the week and the type of gas. Include the marginal distributions. Type of Day Weekday 76.6% Weekend: 23.4% Grade of Gasoline Premium: 21.4% Plus: 14.9% Regular: 63.7%

4. C HAPTER 5 P ROBLEM 39( A ) The mosaic plot represents the contingency table with areas.

5. C HAPTER 5 P ROBLEM 39( B ) Conditional distribution of purchase type for weekday purchases. Premium: 19% Plus: 15% Regular: 66%

6. C HAPTER 5 P ROBLEM 39( C ) Conditional distribution of premium for weekday and weekend purchases. Weekday: 67% Weekend: 33%

7. C HAPTER 5 P ROBLEM 39( D ) Does the difference in parts (b) and (c) indicate association? No. These conditional distributions are not directly comparable. One refers to the type of gas given that the purchase happens on the weekday, whereas the second refers to the timing of the purchase given that the premium purchases of regular gas was bought. To illustrate association, one can, for example, compare the conditional distribution of regular gas to the answer in part c. For regular purchases 448/663 = 80% occur on weekdays, compared to 67% of premium purchases.

8. C HAPTER 5 P ROBLEM 39( D ) The mosaic chart does indicate a relationship:

9. C HAPTER 5 P ROBLEM 39( E ) When should the owner be around to meet Premium customers? Weekends have a greater concentration of Premium customers compared to weekdays, although weekdays have more Premium/overall customers.

10. C HAPTER 5 P ROBLEM 43 Owner Satisfaction A marketing survey of car owners was presented in two ways.11 One wording asked the customer whether he was satisfied with his car. The other asked the customer whether he was dissatisfied. The data table has two variables, one indicating the wording of the question and one giving the level of reported satisfaction.

11. C HAPTER 5 P ROBLEM 43( A ) Contingency table with marginal distributions. The marginal distributions are: Satisfaction Very dissatisfied: 6.8% Somewhat dissatisfied: 6.6% Somewhat satisfied: 31.3% Very satisfied: 55.3% Question Wording Dissatisfied: 49.7% Satisfied: 50.3%

12. C HAPTER 5 P ROBLEM 43( A ) The mosaic chart represents the cell probabilities as areas and the marginal distribution for the question wording is on the right-hand side:

13. C HAPTER 5 P ROBLEM 43( B ) Which group reported being more satisfied? Combine the first two columns of the table. If the question used the word satisfied, (139+82)/243 = 91% were satisfied. If the question used the word dissatisfied, then the percentage satisfied dropped to (128+69)/240 = 82%.

14. C HAPTER 5 P ROBLEM 43( C ) How should company word the question to produce an add? Phrase the question in a positive sense using the word satisfied. Wording puts the notion of being satisfied in the customers mind rather than encouraging the customer to think of reasons that he or she might not be satisfied.

15. C HAPTER 5 P ROBLEM 54 These data compare the on-time arrival performance of flights on American and Delta. The table shows the status of 17,064 arrivals during January 2006.

16. C HAPTER 5 P ROBLEM 54( A ) On the basis of this initial summary, find the percentages (row or column) that are appropriate for comparing the on-time arrival rates of the two airlines. Which arrives on time more often? American

17. C HAPTER 5 P ROBLEM 54( B ) Are there lurking variables by destination? Yes. Atlanta flights are the most likely to be delayed and American hardly ever flies there. American flights concentrate in Las Vegas and San Diego, which are more likely to be on time.

18. C HAPTER 5 P ROBLEM 54( C ) Is Destination a lurking factor behind the original table? Yes. Delta’s overall percentage is weighed down by the Atlanta airport, where it does a majority of its business. Delta is actually more likely to be on time at every location.