Stat 402 B – Exam 1 Take-home Problem
Due at the beginning of the exam on Friday, February 20, 2015
1. [25 pts] The emerald ash borer, Agrilus planipennis, is a wood-boring insect
originally from northeastern Asia. The emerald ash borer was introduced to the
United States, probably in infested wood pallets, sometime around 2000. Over the
past 15 years it has spread from Michigan east to Maryland and west to Iowa.
Because the emerald ash borer destroys ash trees it infests, coming up with a way to
control the borer is of interest to entomologists and foresters. One possible biological
control proposed is spraying infested trees with the fungus, Beauveria bassiana strain
GHA. If the borers are infected with the fungus their life span may be shortened
enough so that they do not breed and thus do not produce a future generation. In
order to investigate the effectiveness of the fungus, a greenhouse trial was conducted
by entomologists at a large Midwestern university. Emerald ash borer infested ash
trees were cut down and the trees were cut into 60-cm logs in winter and held at 4 C
until the summer. In summer, logs were put in an incubator that simulated
summertime temperature (24 C), humidity (50-60%) and hours of light and dark
(16:8) for 28 days. Logs were removed from the incubator and sprayed with a
suspension that contained the fungus. There were four different suspensions; 0 ml,
1.25 ml, 2.5 ml and 3.75 ml of a commercially available form of the fungus was used
to make a 20 ml suspension. After being sprayed each log was put in an individual
cage. As the emerald ash borers emerged from the logs, the entomologists marked
each borer so that the life span (days from emergence to death) could be recorded.
For each log different numbers of borers emerged.
a) [2] What are the conditions of the experiment?
b) [2] What are the experimental units for the experiment?
c) [2] What is the response?
d) [2] Identify an outside variable that is controlled in this experiment and explain
how it is controlled.
e) [2] Is there a control group for this experiment? Explain briefly.
f) [3] Why is having a control group important for this experiment?
g) [2] How many experimental units would you need for this experiment if you
wanted to be able to detect a 1 standard deviation difference in population means
with Alpha = 0.05 and Beta = 0.10?
h) [2] The experiment was run with 12 experimental units. With Alpha = 0.05 and
Beta = 0.05, what is the size of the detectible difference in population means?
i) [5] Explain how you would use JMP to randomly assign the treatments to 12
experimental units. Turn in your JMP data table that shows the random
assignment of treatments to experimental units.
j) [3] Suppose that at the end of the experiment the mean response was greatest for
the 0 ml suspension and was statistically different from the other suspensions.
Additionally, the mean responses for the 1.25 ml, 2.5 ml and 3.75 ml suspensions
were not statistically different. What generalization can you make?