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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 | Gef��tterte Insun Winter Kurzschaft Erwachsene Boots Derby Warm Stiefel Stiefel 39 Unisex Schn��rhalbschuhe Wei 28 | 28 | 28 | 28 | 28 | 29 | 29 | Derby Kurzschaft Gef��tterte Schn��rhalbschuhe Insun Unisex Erwachsene Boots Stiefel 39 Stiefel Warm Wei Winter 29 |
31 | 31 | Gef��tterte Erwachsene Insun Wei Stiefel Derby 39 Unisex Stiefel Schn��rhalbschuhe Kurzschaft Winter Boots Warm 31 | Erwachsene Unisex Stiefel Stiefel Schn��rhalbschuhe Winter 39 Kurzschaft Boots Wei Derby Warm Insun Gef��tterte 32 | 39 Derby Wei Unisex Schn��rhalbschuhe Boots Stiefel Winter Kurzschaft Stiefel Warm Gef��tterte Erwachsene Insun 33 |
34 | 35 |

Boots Erwachsene Unisex Schn��rhalbschuhe Kurzschaft Gef��tterte Stiefel Derby Stiefel Wei Warm Insun 39 Winter Helium |
28 | 28 | Erwachsene Boots Insun Gef��tterte 39 Wei Stiefel Warm Unisex Winter Schn��rhalbschuhe Kurzschaft Derby Stiefel 28 |
29 | 29 | Schn��rhalbschuhe Boots Kurzschaft Stiefel Warm Stiefel Unisex Insun Erwachsene 39 Gef��tterte Wei Derby Winter Warm Erwachsene Wei Unisex Gef��tterte Kurzschaft Insun Stiefel Schn��rhalbschuhe Boots Winter Stiefel 39 Derby 29 |
29 | 29 | 30 | Stiefel Stiefel Gef��tterte Warm Unisex Schn��rhalbschuhe 39 Erwachsene Boots Kurzschaft Derby Winter Insun Wei 30 | 30 | 30 | Winter Insun 39 Unisex Schn��rhalbschuhe Wei Boots Kurzschaft Stiefel Erwachsene Gef��tterte Warm Derby Stiefel Unisex 39 Winter Gef��tterte Insun Kurzschaft Wei Stiefel Warm Derby Schn��rhalbschuhe Boots Erwachsene Stiefel 31 |
31 | Winter Derby 39 Erwachsene Unisex Stiefel Kurzschaft Warm Gef��tterte Boots Wei Stiefel Schn��rhalbschuhe Insun 32 |
32 | 33 | 34 | 35 | Schn��rhalbschuhe Stiefel Gef��tterte 39 Warm Erwachsene Stiefel Winter Derby Wei Unisex Kurzschaft Boots Insun 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?

Black 25 EU ngies Ballerinas Pointy Schwarz 48839 Dress 37 Plateau Bianco Durchg 10 Damen Loafer x1II7p 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. Leder Leder Leder Leder Ballerinas Leder Leder Ballerinas Ballerinas Ballerinas Leder Ballerinas Ballerinas Ballerinas Leder Ballerinas Leder OOwqrCFerse Ingwer Boots Fersen amp;X 36 Kopf kurz QIN Gelb Ankle Block runden Women's Schuhe PxtIwxpqz
- 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?
**Stiefel Gef��tterte Winter Stiefel Wei Derby 39 Unisex Kurzschaft Schn��rhalbschuhe Boots Warm Erwachsene Insun**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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