9.2 Paper aircraft confidence interval

An El Niño spring returns for the first time since 2016. I was so excited to get data from another El Niño season that I went ahead with the exercise despite rain bands crossing campus. The drought portion of this El Niño seems to have ended early. To deal with the mud and wet I brought along a bath towel, took off my shoes and socks, rolled up my pants. I also brought paper towel to clean up the tape measure. 


Before the paper aircraft were launched I wrote on the board that the mean flight distance would be 561 centimeters. I knew that because of the El Niño I would be wrong this term. The mean flight distance for El Niño years is actually 371 centimeters. For La Niña and neutral years the mean flight distance is 572 centimeters. This is due to the winds that arrive with an El Niño spring.  

If one combines all years, El Niño and La Niña, then the mean flight distance before class was 561 centimeters. Because I have always run this exercise against the all seasons population mean, I put the population mean of 561 cm on the board before class. The new data from this term dropped the population mean to 556 centimeters after the class was over.

I had each student make and throw three paper aircraft to offset the low attendance. 


Planes were picked up before I could photograph their location. Two planes were blasted back over the cover walkway and landed to the south of the water fountain. One can be seen on the roof at the right.

One airplane was carried all the down to the cycad. 

The walkway rooftop airplane. The sample size would turn out to not be a multiple of three, not all aircraft were accounted for. 


The 95% confidence interval did not include the pre-existing, known population mean of 561 centimeters. 


The distribution of flight distances indicates the nature of the challenge in reaching 561 cm.


The blue line is the data distribution if the data is redistributed as a normal distribution using the sample mean and the sample standard deviation. The red line is the sampling distribution of the means based on the sample mean and using the sample standard deviation to calculate the standard error of the mean.


The above chart indicates the difference between the population mean and the 95% confidence interval for the sample.


The average flight distance during the previous El Niño was 371 centimeters when averaging the two section averages. The sample sizes are different, but this introduces only a two centimeter difference in the mean.

Comments

Post a Comment

Popular posts from this blog

Plotting polar coordinates in Desmos and a vector addition demonstrator

Image
In an earlier post I noted that Desmos did not directly plot polar coordinates. Not only was I incorrect, but Desmos responded to my blog to correct me! Although I had at some point seen that one could define a function f(x)=3x+5 and then have Desmos calculate f(6), I had not absorbed how this might be used to plot polar coordinates. The above works beautifully . Realizing that I could effectively program Desmos, I applied this thinking to demonstrating how to add two vectors when given the magnitudes m and the direction angles theta. The graph calculates the i and j components for the two vectors and then adds the vectors, graphically displaying the result while also providing information on the magnitude and direction of the vector sum. m1 and theta1 are the magnitude and direction angle for one of the two vectors, m2 and theta2 are the magnitude and direction for the other vector. All four are dynamically interactive and can be changed. The diagram purports to illustra
Read more

Setting up a boxplot chart in Google Sheets with multiple boxplots on a single chart

Image
The  Google Statistics  add-on for Google Sheets can display multiple boxplots in a single chart. The key is the layout of the data. One column should be the variable by which the data is to be grouped, the other column should be the data to be box plotted. Set up the Statistics add-on with the data to be plotted as the variable, and the grouping column as the "by" variable. In this image I had deselected all but the boxplot option, the result was the appearance of the Moment, Standard errors, and Confidence intervals options. The default is apparently a 95% confidence interval for the mean. The result is multiple boxplots on a single chart with a common scale. The new tab that is created also quotes 95% confidence intervals for the mean. Note that as of 2018 the Google Statistics add-on cannot be found by search in the add-ons. In addition, as of May 2018 the add-on no longer verifies, possibly due to the add-on not having been updated since August 2017. One may ha
Read more

Traditional food dishes of Micronesia

Image
Clara, Jennette, and Joanie presented ground hard taro cooked in an umw, effectively a hot rock oven. Pohnpeian: rotama. Pingelapese: sero. Mwoakillese: rodma. Mortlockese: Amahd. Kosrae: rodoma. After cooking in an umw the rotama is pounded with the petiole of a palm frond. Rotama is made from hard or swamp taro, known as mwahng on Pohnpei, mweian on Pingalap, pula in Mortlockese, and pahsruhk on Kosrae. In traditional times on the outer islands the women had primary responsibility for tending the taro while the men handled fishing and climbing tasks. Joesen and Noeleen presented fermented breadfruit from the outer islands of Yap such as Woleai and Eauripik. The raw ingredients were actually brought in from Yap, Noeleen prepared the maare.  The leaf wrap is ti leaf - Cordyline fruticosa. Pauleen, Barnson, Trisha, Verginia, Con-ray, and Maylanda from Kitti, Pohnpei brought in mahi umw, koahpnoair koakihr, and uht sukusuk. Above is breadfruit umw, mahi umw, one o
Read more