Airplane Distance Confidence Intervals
In the Spring of 2012 the MS 150 Statistics students threw paper aircraft off of the second floor balcony. I measured the distance to each plane from the building - the distance perpendicular to the face of the building. The average distance was 627 centimeters. I was curious as to whether that average could be "captured" by repeating the exercise section-by-section this fall 2013 term.
Unbeknownst to me, a student grabbed some images of my measuring in light rain, posted to FaceBook, and tagged me. The students know that I am "FaceBook" friendly. With their permission I grabbed the shots for this blog.
When I embarked on this I had absolutely no idea whether repeating the experiment would capture the former population mean distance. I thought that if statistics worked as I expected, then I had a 95% chance of capturing the mean. In three sections the odds of any one section not including the mean was certainly more than 5%, but one tends to feel safe until the green jelly bean (for those who need this explained).
This worked well given that Monday I had engaged in the FiboBelly exercise which had shown that the long measure divided by the short measure is not 1.618.
The raw data is in a Google Docs spreadsheet. As might be noted in the following table, all three sections - 8:00, 9:00, and 10:00 - included the 627 centimeter mean from spring 2012. Even the narrower all sections confidence interval captured 627 centimeters.
I suspect that the key to this exercise is simply the large coefficient of variation - an average coefficient of variation of 72% ensures that confidence interval will remain broad. As noted in the box plot the minimum distance was often zero - planes that circled back and landed under the launch location. In Spring 2012 one plane flew backward onto the first floor porch yielding a negative distance.
My thanks to MA for photographing the exercise and thus spurring me to document the exercise in my blog. The tools used in class included Gnumeric, LibreOffice.org, and Google Docs.
Unbeknownst to me, a student grabbed some images of my measuring in light rain, posted to FaceBook, and tagged me. The students know that I am "FaceBook" friendly. With their permission I grabbed the shots for this blog.
When I embarked on this I had absolutely no idea whether repeating the experiment would capture the former population mean distance. I thought that if statistics worked as I expected, then I had a 95% chance of capturing the mean. In three sections the odds of any one section not including the mean was certainly more than 5%, but one tends to feel safe until the green jelly bean (for those who need this explained).
The raw data is in a Google Docs spreadsheet. As might be noted in the following table, all three sections - 8:00, 9:00, and 10:00 - included the 627 centimeter mean from spring 2012. Even the narrower all sections confidence interval captured 627 centimeters.
| Statistic | m8 | m9 | m10 | All |
| n | 18 | 23 | 31 | 72 |
| mean | 572 | 745 | 831 | 739 |
| sx | 414 | 479 | 644 | 546 |
| SE | 98 | 100 | 116 | 64 |
| 2 * SE | 195 | 200 | 231 | 129 |
| mean - 2 SE | 377 | 545 | 599 | 610 |
| mean + 2SE | 767 | 945 | 1062 | 867 |
| Pop mean for fall 2013: | 739 | |||
I suspect that the key to this exercise is simply the large coefficient of variation - an average coefficient of variation of 72% ensures that confidence interval will remain broad. As noted in the box plot the minimum distance was often zero - planes that circled back and landed under the launch location. In Spring 2012 one plane flew backward onto the first floor porch yielding a negative distance.
My thanks to MA for photographing the exercise and thus spurring me to document the exercise in my blog. The tools used in class included Gnumeric, LibreOffice.org, and Google Docs.
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