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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 | 225 EU35 Party Red Court Brautschuhe Spitze Stilett Schuhe Abschlussball Heels Hochzeit Damen High ZPFFE Schl��pfen 28 | 28 | 28 | 28 | 28 | 29 | 29 | Heels High Court Abschlussball Hochzeit Red Damen Party Schl��pfen 225 Stilett Spitze Schuhe Brautschuhe EU35 ZPFFE 29 |
31 | 31 | Heels Party Hochzeit 225 Schuhe Brautschuhe High Abschlussball Court EU35 Spitze Schl��pfen ZPFFE Stilett Damen Red 31 | High Stilett Red Abschlussball Schl��pfen Court Party Spitze Schuhe Heels Hochzeit Brautschuhe 225 EU35 ZPFFE Damen 32 | Hochzeit Court Damen High Stilett Heels Schl��pfen Spitze Red ZPFFE EU35 Schuhe Party 225 Abschlussball Brautschuhe 33 |
34 | 35 |

Hochzeit Spitze Heels High Abschlussball Damen ZPFFE Red Schuhe Brautschuhe Schl��pfen 225 Stilett Court Party EU35 Helium |
28 | 28 | 225 EU35 Party Red High Court Damen Hochzeit Stilett Brautschuhe Schuhe Heels Abschlussball Spitze Schl��pfen ZPFFE 28 |
29 | 29 | High Heels Damen EU35 225 Hochzeit Brautschuhe Schuhe Abschlussball Party Spitze Red ZPFFE Court Schl��pfen Stilett Spitze Schl��pfen Brautschuhe ZPFFE Abschlussball Red Heels Stilett Hochzeit High Court Schuhe EU35 Party 225 Damen 29 |
29 | 29 | 30 | High Party Red Heels Abschlussball Brautschuhe Damen Spitze EU35 ZPFFE 225 Hochzeit Schuhe Court Schl��pfen Stilett 30 | 30 | 30 | Abschlussball Schuhe Stilett Schl��pfen Heels Spitze Damen 225 Hochzeit Brautschuhe EU35 Red ZPFFE Party Court High Party High Schl��pfen Spitze Stilett ZPFFE Court Brautschuhe Hochzeit EU35 Schuhe 225 Abschlussball Damen Red Heels 31 |
31 | ZPFFE Brautschuhe Abschlussball Hochzeit Heels Court Red Stilett Schuhe 225 Spitze EU35 Damen Schl��pfen High Party 32 |
32 | 33 | 34 | 35 | Red EU35 Party Damen Stilett Hochzeit ZPFFE Court Abschlussball Spitze Schuhe Schl��pfen 225 High Brautschuhe Heels 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?

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- 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?
**Brautschuhe 225 Court Damen Stilett Schuhe Heels High Red Hochzeit Schl��pfen EU35 ZPFFE Spitze Party Abschlussball**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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