Homework 3 (30 points)
STAT 310
Name(s) ___SOLUTION_____________
Due: Wednesday, February 27th by 4pm
1. An entomologist conducted an experiment on the drinking rate energetics of honeybees to
determine the effects of ambient temperature and viscosity of the liquid on energy
consumption by the honeybee. The temperature levels were 20o, 30O and 40o. This viscosity of
the liquid was controlled by the sucrose concentrations, which were 20, 40 and 60 percent of
total dissolved solids in the drinking liquid for the bees. The entomologist recorded the energy
expended by the bees as joules/second. The data are given in the file Honeybees.jmp on the
course website.
a. Give the statistical model for this scenario. Be sure to fully explain each component.
(4 points)
yijk = µ + αi + βj + αβij + εijk i = 1, 2, 3; j = 1, 2, 3; k = 1, 2, 3 where
yijk is the energy expended from the kth honeybee getting the ith temperature and jth
sucrose concentration
µ is the overall mean energy expended
αi is the effect of the ith temperature
βj is the effect of the jth sucrose concentration
αβij is the interaction effect of the ith temperature and the jth sucrose concentration
εijk is the random error associated with the kth observation getting the ith treatment
and the jth sucrose concentration
b. Determine whether a significant interaction exists between temperature and viscosity of
the liquid. Based on your answer, should you proceed by looking at the interaction or
main effects? Include the appropriate F-statistic and p-value associated with
determining whether the interaction is significant. Provide a detailed sketch of or paste
your JMP output below. (4 points)
F = 7.4961
p-value = 0.0010
There is a significant temperature and viscosity interaction so we should
continue by looking at the interaction.
1
c. Using appropriate methods, determine whether or not the assumptions of constant
variance and normality have been violated. Provide a detailed sketch of or paste your
JMP output below. (3 points)
Normality – Assumption of normality has not been violated. The points follow
the reference line rather well and the histogram is approximately bell-shaped.
Constant Variance – Assumption has not been violated. Horizontal band is
present.
d. Depending on your answer to part b, carry out the remainder of the analysis. That is, if
you found significant effects, where do the differences exist? Provide a detailed sketch
of or paste your JMP output below. (4 points)





There appears to be a significant difference
between the 40 degree temperature/60% sucrose
treatment and everything else.
The 30/60 and 40/40 treatments are not
significantly different from one another.
The 40/40 and 30/40 treatments are not
significantly difference from one another.
The 20/60, 40/20, 30/20, and 20/40 treatments are
not significantly different from one another.
The 20/40 and 20/20 treatments are not
significantly different from one another.
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2. A field plot experiment was conducted to evaluate the interaction between timing of nitrogen
application to the soil (early, optimum, late) and two levels of a nitrification inhibitor (none, 0.5
lb/acre). The inhibitor delays conversion of ammonium forms of nitrogen into a more mobile
nitrate form to reduce leaching losses of fertilizer-derived nitrates. The nitrogen was supplied
as pulse-labeled 15N through a drip irrigation system at an early, an optimum, and a late date of
application. The data collected are percent of 15N taken up by sweet corn plants grown on the
plots and can be found in the file Nitrogen.jmp on the course website.
a. Give the statistical model for this scenario. Be sure to fully explain each component.
(4 points)
yijk = µ + αi + βj + αβij + ρk + εijk i = 1, 2, 3; j = 1, 2; k = 1, 2, 3
yijk is the percent of 15N in the kth block for the ith timing and the jth inhibitor
µ is the overall mean percent of 15N
αi is the effect of the ith timing
βj is the effect of the jth inhibitor
αβij is the interaction effect of the ith timing and the jth inhibitor
ρk is the effect of the kth block
εijk is the random error associated with the kth block for the ith timing and jth inhibitor
b. Determine whether a significant interaction exists between timing of nitrogen
application to the spoil and levels of nitrification. Based on your answer, should you
proceed by looking at the interaction or main effects? Include the appropriate Fstatistic and p-value associated with determining whether the interaction is significant.
Provide a detailed sketch of or paste your JMP output below. (4 points)
F = 27.1189
p-value = 0.0001
There is a significant interaction between timing of nitrogen and the level of
nitrification. Therefore, the interaction should be examined.
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c. Using appropriate methods, determine whether or not the assumptions of constant
variance and normality have been violated. Provide a detailed sketch of or paste your
JMP output below. (3 points)
Normality – The assumption of normality seems to hold. The points follow the
reference line and the histogram
Constant Variance – There could be a problem with constant variance, but the
pattern isn’t too prominent.
d. Depending on your answer to part b, carry out the remainder of the analysis. That is, if
you found significant effects, where do the differences exist? Provide a detailed sketch
of or paste your JMP output below. (4 points)
The Early/None treatment is
significantly different from all other
treatment combinations.
4