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April 16, 2014

Homework Help: Statistics

Posted by Ryan on Monday, May 21, 2012 at 4:44pm.

Does a football filled with helium travel farther than one filled with ordinary air? To test this, the Columbus Dispatch conducted a study. Two identical footballs, 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 (the helium-filled or the air-filled football) he was kicking. The distance of each punt was recorded. Then another trial was conducted. A total of 39 trails were run. Here are the data for the 39 trials, in yards that the footballs traveled. The difference (helium minus air) is the response variable.

Helium 25 16 25 14 23 29 25 26 22 26
Air 25 23 18 16 35 15 26 24 24 28
Difference 0 -7 -7 -2 -12 14 -1 2 -2 -2
Helium 12 28 28 31 22 29 23 26 35 24
Air 25 19 27 25 34 26 20 22 33 29
Difference -13 9 1 6 -12 3 3 4 2 -5
Helium 31 34 39 32 14 28 30 27 33 11
Air 31 27 22 29 28 29 22 31 25 20
Difference 0 7 17 3 -14 -1 8 -4 8 -9
Helium 26 32 30 29 30 29 29 30 26
Air 27 26 28 32 28 25 31 28 28
Difference -1 6 2 -3 2 4 -2 -2 -2

(a) Examine the data. Is it reasonable to use the t procedures?
(b) If your conclusion in part (a) is “Yes,” do the data give convincing evidence that the helium-filled football travels farther than the air-filled football?

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