The following description is taken from theAnkle Spitze Heels Boots Plateauschuhe Kurze CXQ QIN High amp;X 37 Dunkelgr��n Zehe Frauen Stiletto Stiefel xgBBnqA.

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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 | Heels Block Boots High QIN der Plateauschuhe 36 Ankle rot Runder Frauen amp;X kurze 28 | 28 | 28 | 28 | 28 | 29 | 29 | rot 36 Boots Plateauschuhe Frauen amp;X QIN Block Heels High Ankle Runder kurze der 29 |
31 | 31 | 36 QIN rot Runder amp;X kurze Block Heels High Frauen der Boots Plateauschuhe Ankle 31 | Frauen High amp;X der Plateauschuhe QIN Heels Boots Runder rot Ankle 36 kurze Block 32 | Plateauschuhe kurze 36 Ankle amp;X QIN rot Block Boots der Runder High Heels Frauen 33 |
34 | 35 |

Boots rot QIN der High amp;X kurze Ankle Heels 36 Frauen Block Plateauschuhe Runder Helium |
28 | 28 | amp;X Block Ankle Boots 36 der QIN kurze Heels Runder High Frauen rot Plateauschuhe 28 |
29 | 29 | Plateauschuhe rot Runder 36 QIN kurze Heels Boots Frauen Ankle der High Block amp;X 36 Heels Frauen Plateauschuhe High kurze rot Ankle QIN der Runder Block amp;X Boots 29 |
29 | 29 | 30 | der rot Frauen Heels kurze Plateauschuhe Ankle Boots Block QIN High amp;X 36 Runder 30 | 30 | 30 | der kurze Runder Heels Boots QIN rot Frauen High Ankle 36 Plateauschuhe Block amp;X Frauen der Block Heels Runder High Plateauschuhe Boots QIN Ankle rot amp;X kurze 36 31 |
31 | amp;X 36 Frauen Boots kurze rot Block Ankle der QIN High Runder Heels Plateauschuhe 32 |
32 | 33 | 34 | 35 | der kurze Block Boots amp;X Runder Plateauschuhe Frauen QIN rot 36 Heels High Ankle 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.
**Ankle Heels QIN Frauen rot der 36 Plateauschuhe Runder Boots amp;X kurze Block High**

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?
**High rot Boots QIN Heels der Runder 36 Plateauschuhe amp;X Block Frauen Ankle kurze**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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