Stat 402 B – Exam 1 Take-home Problems
Due in class Wednesday, February 27, 2008
1. [25 pts] For this problem you will make decisions about how to design an
experiment to examine the effect that cooking time and power setting have on the
quality of microwave popcorn. In particular, the cooking times of interest are 3,
3½, 4, and 4½ minutes. The two power settings are 10 (full power) and 7 (70%
power). For the experiment pre-packaged bags of microwave popcorn will be
used.
a) [3] What would you use for a response for this experiment? Be specific.
If your response involves measurement indicate how you would measure.
b) [2] What are the conditions of the experiment?
c) [1] Using factorial crossing, how many treatment combinations are there
in the experiment?
d) [1] What is the experimental material?
e) [4] Name at two outside variables that should be controlled. Indicate how
you would control each of the variables that you mention. Be specific.
f) [2] Name one outside variable related to the pre-packaged bags of
microwave popcorn that you cannot control?
g) [2] What will randomization do with the variability introduced by the
variable that you identified in f)?
h) [2] We wish to be able to detect a difference in cooking time sample
means equal to 0.9 standard deviations with Alpha = 0.05 and Beta = 0.10.
How many pre-packaged bags of microwave popcorn do we have to buy?
i) [2] We only have enough money to buy 32 pre-packaged bags of
microwave popcorn. Give two combinations of Alpha, Beta, and
Δ
σ
for
comparing the power setting sample means that can be achieved with this
number of bags.
j) [3] You have 32 pre-packaged bags of microwave popcorn. You put all of
them into a big container. Explain how you could assign packages to
conditions completely at random. You cannot use a random number table
or column shuffle to do this.
k) [3] Use Column Shuffle in JMP or some other random mechanism to
produce a single random sequence for the numbers 1 to 32. Include this
with your take home answers and explain how to use this to produce a
randomized order in which to pop the 32 bags of popcorn.