Stat 402 B – Exam 2 Take-home Problem
Due at the beginning of the exam on Monday, April 9, 2012
1. [30 pts] For this problem you will make decisions about how to design an experiment that
extends the quasi-experiment on batteries presented in the take-home problem for Exam 1.
Battery brand is an observational factor that cannot be assigned at random to experimental
material. In particular, the battery brands are Energizer, Duracell, and Radio Shack. You
have a simple circuit that can accommodate a single battery attached to a small electric
motor. There is a switch in the circuit that can be used to turn on and off the motor. A
second factor of interest is the amount of time the battery is in the circuit with the motor
turned on. There are 4 levels for this factor: 0 minutes, 30 minutes, 60 minutes and 90
minutes. A time of 0 minutes means that a battery is placed in the circuit and immediately
removed without turning on the motor. We are interested in differences amongst the brands
of batteries, the effect of time on battery voltage and any possible interaction between brands
and time. The response will be the voltage of the battery when it is removed from the circuit
after the specified time. Size C alkaline batteries from each brand will be used in the
experiment.
a) [2] What are the conditions of the experiment?
b) [2] What are the treatments? List all treatments.
c) [2] If you were to conduct this experiment as a completely randomized design, how could
you achieve replication within this experiment?
d) [2] Suppose you have 16 Energizer, 16 Duracell and 16 Radio Shack batteries. In a
balanced completely randomized design, with Alpha = 0.10 and Beta = 0.10 what size
difference in brand means will you be able to detect?
e) [2] Suppose you have 16 Energizer, 16 Duracell and 16 Radio Shack batteries. In a
balanced completely randomized design, with Alpha = 0.05 and Beta = 0.05 what size
difference in time means will you be able to detect?
f) [4] Use Col Shuffle in JMP to produce a single random sequence for the numbers 1 to 48.
Explain how to use this to produce a randomized order in which the 16 Energizer, 16
Duracell and 16 Radio Shack batteries will be tested at the various times. Attach the JMP
data table that shows the randomized order of the treatments tested.
It will take a fairly long time to get a single replication of all the treatment combinations in
this experiment (over 9 hours). You can probably do only a single replication each day.
Additionally, a motor will not last more than 9 hours due to the wear caused by the heat
generated while running the motor for extended periods of time. Luckily, in addition to the
motor in the circuit you have 3 replacement motors.
g) [4] Explain how you can use a randomized complete block design to overcome the
difficulty of one replication in a day and a motor lasting at most 9 hours.
h) [6] Explain how to use JMP to randomly assign treatments within each block. Attach a
single JMP data table that shows the random assignment of treatments within four blocks
i) . Hint: It may be easier to make several JMP tables and combine those into a single table
to hand in.
j) [3] Give the partial analysis of variance table for your randomized complete block design.
Include all sources of variation and degrees of freedom in the table.
k) [3] Describe what is contributing to the “error” variation in the randomized
complete block design within the context of the problem.