In: Statistics and Probability
How do competing airline carrier fares compare? A frequent flyer investigated round-trip fares for non-stop travel from Philadelphia to 10 different U.S. destinations on Southwest Airlines and US Airways. The following data was collected:
| 
 Southwest Fare ($)  | 
 US Airways Fare ($)  | 
| 
 706  | 
 706  | 
| 
 718  | 
 674  | 
| 
 980  | 
 980  | 
| 
 1078  | 
 1284  | 
| 
 654  | 
 654  | 
| 
 820  | 
 748  | 
| 
 820  | 
 728  | 
| 
 832  | 
 822  | 
| 
 1114  | 
 1918  | 
| 
 1138  | 
 1918  | 
a. At the .05 level of significance, is there evidence of a difference in the mean round-trip fare between Southwest Airlines and US Airways?
b. What assumption is necessary about the population distribution in order to perform this test?