WeBWorK Standalone Renderer

O.L. Davies (1960, pp. 258-267) describes an experiment exploring the effect of certain factors on the percentage yield of a nitration process, the product of which forms the basis of various medicinal products. The three factors investigated were as follows, each with two levels as described below.

The time of addition of nitric acid: 2 hours or 7 hours.
The time of stirring: either 1/2 hour or 4 hours.
Heel: either present or absent.

Heel is a slang term for residual product left in the container from the previous batch. It may not always be possible to completely remove this residue, which could possibly impact the yield in the succeeding batch.

Suppose the data were as displayed below:

$\begin{array}{c r} & \text{No Heel} \ \ \ \ \ \ \ \ \ \ \ \ \ \text{With Heel} \ \ \ \ \ \ \ \ \ \ \ \\ & \text{Time of addition of nitric acid} \ \ \ \ \ \ \ \ \ \ \\ \text{Time of stirring} & \begin{array}{c | c c | c c} & \text{2 hours} & \text{7 hours} & \text{2 hours} & \text{7 hours} \\ \hline \text{1/2 hour} & & & & \\ \text{4 hours} & & & & \\ \end{array} \end{array}$

Part a)
Using the R command interaction.plot (or otherwise) create three two-way interaction plots to investigate possible interactions between the three factors. Which of the following is the interaction plot between the time of addition of nitric acid and time of stirring?



A		B



C

(Click on a graph to enlarge it.)

Part b)
Find the main effect of the time of addition of nitric acid (giving your answer to two decimal places; positive answers only).

Part c)
Use R to compute the ANOVA table for the additive model. That is, the model with no interaction terms. Provide the F statistic for the effect of the time of addition of nitric acid (to three decimal places).

Part d)
Provide the P-value for your test statistic in Part c), to three decimal places.

Part e)
Which of the following is a significant main effect when testing at the 5% significance level (select all that apply)?

Davies, O.L. (1960): The Design and Analysis of Industrial Experiments. Oliver and Boyd.

You can earn partial credit on this problem.