9.2 Paper aircraft confidence interval

 This term a revised Desmos provided a visualization of the experiment. A new set of header variables and changes in the functions below automatically generate the graphic. 

Desmos

Spreadsheet

This term I stumbled into the FORMULATEXT function which generates an automatic reporting of the functions in use. The dynamically updating calculations is also displayed.  The new population mean is now 556.61 or 557 cm. 

An explainer shared to the online students:

Today the residential class threw 18 paper airplanes from the second floor of the A building on the national campus. The 18 airplanes were predicted to fly an average of 556 cm away from the building based on a pre-existing known population mean flight distance. This population mean was based on 868 aircraft thrown during 44 prior terms back to 2012.

The aircraft flew a sample mean distance of 607 cm with a sample standard deviation of 514 cm. The standard error of the mean was 121 cm. With a t-critical of 2.110 [=TINV(0.05,18-1)], the 95% confidence interval went from 351 cm to 862 cm, which included the known population mean of 556 cm. This means that 556 cm is a possible population mean distance for the 18 planes thrown fall 2024.

Spreadsheet with calculations:
https://docs.google.com/spreadsheets/d/1MlFWbkVKBwCViiCo0dxAZKXvu9Uph__3XxXzFlYEUv8/edit

Note that you cannot edit the spreadsheet, but you can see the formulas I used to make the calculations of the 95% confidence interval for the paper airplanes.

Number line view:
<----[lower:351==popMean:556==sampleMean:607==upper:862]--->

Desmos diagram of theory underneath the fall 2024 data:
https://www.desmos.com/calculator/0jbeqpethn

When I predicted that the planes would fly an average of 556 cm away from the building, I was wrong. They flew an average of 607 cm. When I shifted to saying "The sample supports a population mean flight distance of 351 to 862 cm" I became right because 556 cm is between 351 and 862 cm. If I do not know the actual population mean, then I can be 95% confident that the population mean is between 351 and 862.



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