In: Statistics and Probability
The Columbus Dispatch conducted a study. Two identical football, one filled with helium and one filled with ordinary air, were used. A casual observer was unable to detect a difference in the two footballs. A novice kicker was used to punt the footballs. A trial consisted of kicking both footballs in a random order. The kicker did not know which football he was kicking. The distance of each punt was recorded, then another trial was conducted. A total of 39 trials were run. Do the data indicate that helium-filled footballs travel farther than air-filled footballs? Give a confidence interval and significance test. (Data: FTBALL)
| Helium | Air | Difference | 
| 25 | 25 | 0 | 
| 16 | 23 | -7 | 
| 25 | 18 | 7 | 
| 14 | 16 | -2 | 
| 23 | 35 | -12 | 
| 29 | 15 | 14 | 
| 25 | 26 | -1 | 
| 26 | 24 | 2 | 
| 22 | 24 | -2 | 
| 26 | 28 | -2 | 
| 12 | 25 | -13 | 
| 28 | 19 | 9 | 
| 28 | 27 | 1 | 
| 31 | 25 | 6 | 
| 22 | 34 | -12 | 
| 29 | 26 | 3 | 
| 23 | 20 | 3 | 
| 26 | 22 | 4 | 
| 35 | 33 | 2 | 
| 24 | 29 | -5 | 
| 31 | 31 | 0 | 
| 34 | 27 | 7 | 
| 39 | 22 | 17 | 
| 32 | 29 | 3 | 
| 14 | 28 | -14 | 
| 28 | 29 | -1 | 
| 30 | 22 | 8 | 
| 27 | 31 | -4 | 
| 33 | 25 | 8 | 
| 11 | 20 | -9 | 
| 26 | 27 | -1 | 
| 32 | 26 | 6 | 
| 30 | 28 | 2 | 
| 29 | 32 | -3 | 
| 30 | 28 | 2 | 
| 29 | 25 | 4 | 
| 29 | 31 | -2 | 
| 30 | 28 | 2 | 
| 26 | 28 | -2 |