A Student Wants to Build a Paper Airplane That Gets

question 290

Essay

A student wants to build a paper airplane that gets maximum flight distance. She tries
three ways of bending the wing (down, flat, and up) and two levels of nose weight (no and yes
- a paper clip). She randomizes the 12 runs (each condition replicated twice). The analysis
of variance for the 12 runs is shown in the table below along with an interaction plot and
tables of the mean distance for the different wing bends and weights. $$\begin{array}{l}\begin{array} { | l r r r r r | } \hline \text { Source } & \text { df } & \begin{array} { l } \text { Sums of } \\\text { Squares }\end{array} & \begin{array} { l } \text { Mean } \\\text { Square }\end{array} & \text { F-ratio } & \text { P-value } \\\hline \text { Wing Bend } & 2 & 13565.2 & 6782.58 & 152.7 & < 0.0001 \\\text { Weight } & 1 & 6768.75 & 6768.75 & 152.39 & < 0.0001 \\\text { Interaction } & 2 & 186.5 & 93.25 & 2.0994 & 0.2036 \\\text { Error } & 6 & 266.5 & 44.4167 & & \\\text { Total } & 11 & 20786.9 & & & \\\hline\end{array}\\\\\begin{array} { | c c | } \hline \text { Wing Bend } & \begin{array} { c } \text { Expected } \\\text { Mean }\end{array} \\\hline \text { Down } & 145.0 \\\text { Flat } & 182.5 \\\text { Up } & 227.2 \\\hline\end{array}\\\\\begin{array} { | c c | } \hline \text { Weight } & \begin{array} { c } \text { Expected } \\\text { Mean }\end{array} \\\hline \text { No } & 161.2 \\\text { Yes } & 208.7 \\\hline\end{array}\end{array}$$



a. Does an additive model seem adequate? Explain.
b. Write a report on this analysis of the data. Include any recommendations you would
give the student on designing the plane.

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