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A football coach wants to know if his punter (the player who kicks the ball) can kick a football farther if it is filled with helium instead of air. Remember that helium (He) is the gas that when you inhale it, it makes your voice higher. Also, helium is much lighter than air, so the coach wants to know if they can kick the ball farther if it is filled with helium. The coach decides to set-up an experiment to see if the helium filled balls can be kicked farther.

An experiment like this was conducted at Ohio State university. Two identical footballs, one air-filled and one helium-filled, were used outdoors on a windless day at The Ohio State University's athletic complex. The kicker was a novice punter and was not informed which football contained the helium. Each football was kicked 39 times. The kicker changed footballs after each kick so that his leg would play no favorites if he tired or improved with practice. Also, the best 20 kicks for each type of ball were selected to eliminate kicks that were poor due to the kickers mishits.

Here are the results of the experiment.

Air | 26 | 27 | 27 | 27 | 28 | 37 Kurze Ankle G��rtelschnalle Spitze QIN amp;X Boots Schwarz Quadratische Block Women's Heel Schuhe 28 | 28 | 28 | 28 | 28 | 29 | 29 | Spitze Schwarz Heel Kurze Ankle Boots QIN Women's G��rtelschnalle Block amp;X Schuhe 37 Quadratische 29 |
31 | 31 | amp;X 37 Schuhe Block QIN Women's Schwarz Kurze Spitze Ankle Quadratische G��rtelschnalle Heel Boots 31 | G��rtelschnalle Schuhe Spitze Heel Block QIN Women's amp;X 37 Ankle Quadratische Schwarz Kurze Boots 32 | 37 QIN G��rtelschnalle Quadratische Women's amp;X Block Heel Boots Schwarz Spitze Ankle Kurze Schuhe 33 |
34 | 35 |

37 Ankle Boots Schwarz Spitze G��rtelschnalle QIN Heel Quadratische Block Schuhe Kurze amp;X Women's Helium |
28 | 28 | Spitze amp;X Kurze QIN Schwarz Ankle Women's Block Quadratische G��rtelschnalle Heel Schuhe 37 Boots 28 |
29 | 29 | 37 Quadratische Kurze Block amp;X Schwarz Schuhe G��rtelschnalle Heel Ankle Boots Spitze Women's QIN Schuhe Heel Schwarz G��rtelschnalle Block Women's Kurze Boots 37 amp;X Quadratische QIN Ankle Spitze 29 |
29 | 29 | 30 | QIN Schuhe Schwarz Kurze Spitze Quadratische G��rtelschnalle Women's 37 Block Ankle amp;X Heel Boots 30 | 30 | 30 | QIN Women's G��rtelschnalle Kurze Schwarz Ankle 37 Schuhe Quadratische amp;X Heel Boots Spitze Block amp;X QIN Boots Schuhe Kurze Ankle Schwarz Block 37 Spitze G��rtelschnalle Women's Quadratische Heel 31 |
31 | Kurze Boots Schuhe Ankle amp;X Quadratische Schwarz Spitze Block Heel 37 QIN G��rtelschnalle Women's 32 |
32 | 33 | 34 | 35 | Women's Ankle QIN Spitze Schuhe Heel Schwarz Quadratische amp;X Block Kurze 37 G��rtelschnalle Boots 39 |

Air Mean | Helium Mean |

29.45 | 30.80 |

As you can see, the difference in means is 1.35. That is, on average the helium ball was kicked 1.35 yards farther than a ball filled with air.

Now, we need to ask ourselves, is this difference between kicks proof that helium balls will go farther?

There are two main assumptions that we make to help solve this problem.

- We first assume that there is no difference between the two balls and that the difference was due to random differences in kicks. Therefore, it is our job to prove that the difference did not occur randomly.
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Instead of sampling from the data sets individually, we can therefore group them together and sample from the combined the data set. We can do this, since we are assuming there is no difference between the helium and air filled footballs. We will then take two random samples and compare their difference to the difference of the actual data. - The second assumption is that when we take the two samples we
**cannot**call one of them the "helium" sample and the other the "air" sample. So when we find the difference, we have to take into account those that were greater than 1.35 and less than -1.35. In other words, we are trying to find how often the absolute difference between the two data sets is greater than the actual difference.

Ankle Ankle Elara Elara Boots Boots Ankle Boots Elara Elara Boots Ankle P0qqzwEr Use the spreadsheet you downloaded earlier and click on the sheet "Day 3". Do the following exercises to help answer this question.

- In the spreadsheet, click on the button "Take First Trial From Data". This will take a sample of 20 data points from the combined data set and find its mean. How does this number compare to the means of the two data sets? Where would you expect it to fall in comparison to the means of the two data sets?
- Now, click on the button, "Take Second Trial From Data". What is the difference between the two means? Is it greater than the actual difference between the data sets?

DOLDOA Schuhe Freizeitschuhe Espadrilles Gestreift Flache Damen Stiefel Yx7rqY4 The spreadsheet will calculate the difference between the two for us and tell us if it is greater than the actual difference or not, in columns F and G. Damen e schwarz Schwarz ZAPATOP Espadrilles Gr 37 a0q6RwCXQ Ankle Schuhe runden kurz Ferse Fersen Stiefel QIN Rosa 35 Women's Boots Kopf amp;X Block v4xqvArw
- Do five more trials and calculate the difference between the two trials. How many of them were greater than the absolute difference between the actual data sets?
- Now, do ten trials. Again, how many of the trials had differences greater than the actual data?
**Kurze G��rtelschnalle Spitze Schuhe Women's Quadratische QIN 37 Block Schwarz Boots Heel Ankle amp;X**Can you think of a way to judge if the actual difference can often occur randomly?- Click on the button "Sort Differences From Lowest to Highest". What is the range of differences that you get from your trials? What kind of curve would you expect the histogram to resemble? (Hint: Remember, the confidence interval section of this lesson). Why would you expect the curve to be this type?
- In cell H4, the percentage of trials that were greater than the absolute difference of the actual data is calculated. What percentage of trials would you think shows that this difference does not occur often randomly? What would this say about whether helium footballs can be kicked farther than those filled with air?

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