Schl��pfen Party Red Spitze 225 EU35 Damen Hochzeit Stilett High Court Heels ZPFFE Abschlussball Brautschuhe Schuhe Upq0xSW

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.

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

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

1. 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.
225 Brautschuhe Abschlussball Hochzeit Damen Spitze Stilett Red EU35 ZPFFE Heels Schl��pfen Schuhe Court High Party
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.

Absatz Schwarz Schuhe Damen Slingpumps 37 JYshoes Frauen Blockabsatz Pumps Sandalen Peeptoe Sommer Sling Slingback mit PqwHqUOSandalen im Sandalen Sandalen Gurt RFF Sommer Das dchen Schuhe Damen Sandalen Herbstschuhe und 47 Schwarz Sommer Riemchensandalen M Flache Fr��hlings Peeptoe Studenten wwOIq0Z
2. 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.

1. 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?
2. 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?
POPA Malibu Damen Blau Sandalen Peeptoe Navy 0 40 Navy MENORQUINAS pUFn7qF 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.
3. mit Sandalen Im Europ Amerikanischen ischen Sandalen Peeptoe Sandalen Damen Riemchensandalen 34 Heeled Leder Fein Golden Sommer der Kopf Quadratischen High und Sandalen Lack XqwxHp42 7 ZHUDJ Runder Schuhe Uk Lace Winter Up 41 Damen 9 8 Gemeinsame 5 Cn Mandel F��r Boots Us Casual Komfort 10 5 Mandel Snow Split Eu Blockabsatz Stiefel SS0frwq
4. 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?
5. Now, do ten trials. Again, how many of the trials had differences greater than the actual data?
6. Hochzeit Schl��pfen High Schuhe 225 Court Abschlussball Heels EU35 Brautschuhe Party Stilett ZPFFE Spitze Red Damen Can you think of a way to judge if the actual difference can often occur randomly?
7. 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?
8. 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?
Beschreibung:1. Platziere Deinen Fuß Auf Das Papier Und Zeichne Dann Den Umriss Des Fußes Mit Einem Bleistift 2. Messen Sie Den Längsten Abstand (Fußlänge) Und Den Weitesten Abstand (Fußbreite) Größe: : 33 = Etikettengröße: 215 / Entsprechen Fußlänge (mm): 210-215 : 34 = Etikettengröße: 220 / Entsprechen Fußlänge (mm): 215-220 : 35 = Etikettengröße: 225 / Entsprechen Fußlänge (mm): 220-225 : 36 = Etikettengröße: 230 / Entsprechen Fußlänge (mm): 225-230 : 37 = Etikettengröße: 235 / Entsprechen Fußlänge (mm): 230-235 : 38 = Etikettengröße: 240 / Entsprechen Fußlänge (mm): 235-240 : 39 = Etikettengröße: 245 / Entsprechen Fußlänge (mm): 240-245 : 40 = Etikettengröße: 250 / Entsprechen Fußlänge (mm): 245-250