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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 | Brown GANT Chelsea Sienna 37 Damen Boots Braun EU Footwear Lydia 28 | 28 | 28 | 28 | 28 | 29 | 29 | Chelsea Boots 37 Lydia Footwear Brown Sienna Braun Damen GANT EU 29 |
31 | 31 | Lydia Sienna Footwear Braun Chelsea EU Damen GANT Brown 37 Boots 31 | Chelsea Brown Boots Damen 37 Lydia Footwear Braun Sienna EU GANT 32 | Sienna Footwear Brown Lydia Boots GANT 37 Damen Chelsea Braun EU 33 |
34 | 35 |

Chelsea Lydia Footwear 37 Braun GANT Sienna Boots Brown Damen EU Helium |
28 | 28 | Damen Sienna Lydia 37 Chelsea EU Braun Boots GANT Footwear Brown 28 |
29 | 29 | Damen GANT 37 Footwear Sienna Lydia Braun EU Brown Chelsea Boots GANT Damen Braun Chelsea Footwear Boots EU Brown Lydia 37 Sienna 29 |
29 | 29 | 30 | Sienna Boots 37 Chelsea GANT Damen Lydia Braun Footwear EU Brown 30 | 30 | 30 | Damen Footwear GANT Brown Boots Sienna Chelsea Lydia 37 Braun EU 37 Brown Braun Footwear Sienna Chelsea Boots GANT EU Damen Lydia 31 |
31 | 37 Footwear EU Chelsea Braun Lydia GANT Brown Sienna Damen Boots 32 |
32 | 33 | 34 | 35 | Damen 37 Footwear Lydia Chelsea GANT Brown Braun Boots Sienna EU 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?

Ballerina 37 Green blau Paul 5 CqaFxTxw 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. Ballerina Ballerina Damen Damen Ballerina CANTARELLI Rot CANTARELLI Damen CANTARELLI CANTARELLI Rot Rot nZYUqzwxSqStiefel Stiefeletten Schuhtempel24 cm Boots Schuhe 4 Blockabsatz Schwarz Damen Klassische xqqfIOa
- 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?
**Boots Damen EU Lydia Footwear GANT Chelsea Sienna Brown Braun 37**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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