Essex Prescott
Assignment HW6 due 11/06/2015 at 11:59pm PST
STAT300-101 2015W1
1. (1 pt) 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.
A
B
Suppose the data were as displayed below:
Time of stirring
1/2 hour
4 hours
No Heel
With Heel
Time of addition of nitric acid
2 hours 7 hours 2 hours 7 hours
87.1
88.6
86.7
89.4
81.9
83.1
83.5
83.7
C
(Click on a graph to enlarge it.)
Part a)
Using the R commandinteraction.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?
Part b)
Find the main effect of the time of addition of nitric acid (giving
your answer to two decimal places; positive answers only).
?
1
Part c)
Use R to compute the ANOVA table for theadditive 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 e)
Which of the following is a significant main effect when testing
at the 5% significance level (select all that apply)?
• A. The time of addition of nitric acid
• B. The time of stirring
• C. Heel
Part d)
Provide the P-value for your test statistic in Part c), to three
decimal places.
Davies, O.L. (1960):The Design and Analysis of Industrial
Experiments. Oliver and Boyd.
Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America
2
