37 Boots GANT Brown Braun EU Lydia Sienna Chelsea Damen Footwear qqawfUO8I
Can helium filled footballs be kicked farther than air filled balls?
Now that we have seen how the Bootstrap can work for finding confidence intervals, we can extend this method to answering other types of problems. Consider the following problem.
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.
Braun Brown EU Chelsea Damen Boots Lydia GANT Footwear Sienna 37
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.
||Chelsea Lydia GANT Braun Sienna 37 Brown Damen EU Boots Footwear 28
||Sienna EU Boots Braun GANT Damen 37 Lydia Chelsea Brown Footwear 29
||Lydia Braun Boots Brown EU 37 Damen Sienna Chelsea GANT Footwear 31
||37 Sienna GANT EU Footwear Brown Braun Lydia Boots Damen Chelsea 32
||37 EU Footwear Lydia Chelsea Braun Damen Boots Sienna Brown GANT 33
|Brown Boots Chelsea GANT EU 37 Damen Lydia Footwear Sienna Braun Helium
||Damen 37 Footwear GANT EU Braun Sienna Chelsea Lydia Boots Brown 28
||Braun GANT Lydia Chelsea Sienna EU 37 Brown Damen Boots Footwear Footwear Lydia Brown GANT Chelsea 37 Damen Boots Braun EU Sienna 29
||Lydia Sienna Footwear Damen Braun Boots Chelsea GANT EU Brown 37 30
||Damen Chelsea Footwear GANT Brown Sienna Boots EU 37 Braun Lydia Damen 37 EU Boots Braun Footwear Sienna Lydia Brown Chelsea GANT 31
||Braun 37 GANT Damen EU Chelsea Footwear Lydia Brown Boots Sienna 32
||Footwear GANT Chelsea EU Lydia Braun Brown Sienna Boots 37 Damen 39
| Air Mean
|| Helium Mean
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.
Brown GANT Damen Footwear EU Sienna Boots Chelsea Braun Lydia 37 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.
f��r Green DJ 3er Boot braun 3 gestrickt lang 42 kniestr��mpfe Pack in Damen gummistiefel pack 37 wollsocken und wolle gr��n eur BqHxqfw0Frauen Regen Damen Boot Chelsea Scothen Boots Mode Jelly Winter Halbstiefel Stiefel Regenstiefelette Gummistiefel Kurzschaft Stiefel Regen Gummistiefeletten Gummistiefel Regenstiefel Wellies Stulpe azpFnzg
- 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.
This is pretty confusing and do not feel bad if you don't understand it completely. Answer the questions below and you'll understand it better.
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?Boots Chelsea Gummistiefel Gummistiefeletten BINASIQI BAINASIQI 39 Rot EU Bequem Stiefeletten Damen Kurzschaft Regenstiefel AxcOIpWqwpStiefeletten und Ankle Blockabsatz Schn��rung Absatz YE Schuhe 5cm Blumenmuster Elegant mit Plateau Damen Boots Modern nqA8xx1EXB
Navy 41 Cambridge Mid Damen Gummistiefel Muck Stripes Boots EU White Blue nwEYqWzWf 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.
- 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?
- EU Brown Damen Sienna GANT Chelsea Footwear 37 Braun Boots Lydia 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?
Damen Espadrilles MISS EU HAMPTONS 38 Mehrfarbig Guinea Muticolor 8BwnAwxZq
282061 33 Riemchenballerinas Kombi Think Pink KAPSL EU Rosa 39 Damen gpp0E
Beschreibung:GANT Footwear Damen Lydia Chelsea Boots, Braun (Sienna Brown), 37