Take home problems for Exam 3 (this is a take home - only
exam)
1. Researchers are interested in the effect of cake batters and oven
temperatures on the moistness of cakes. They have a very precise oven so that
they can control temperature, but it takes time for it to reach its temperature,
so they conducted the following experiment: They heated the oven to one of three
temperatures (330, 350, 370) and then they baked each of the four cake batters
in the oven on different shelves. Thus each ‘oven run’ gives data on a single
temperature and all four cake batters.
The data are (run, temperature, batter,
moistness) :
1 350 1 81 1 350 2 77 1 350 3 83 1 350 4 73
2 330 1 75 2 330 2 79 2 330 3 80 2 330 4 76
3 370 1 67 3 370 2 73 3 370 3 75 3 370 4 67
4 350 1 76 4 350 2 74 4 350 3 80 4 350 4 75
5 330 1 78 5 330 2 71 5 330 3 76 5 330 4 80
6 370 1 69 6 370 2 69 6 370 3 76 6 370 4 67
Write one or more sentences summarizing your conclusions for each of the
following problems. Your summary should allow a person to understand your
results even if they do not know the software that you used (SAS, R, etc.). Hand
in both your written summary and enough computer output to show your results.
a) Name this design and give the model equation.
b) Conduct tests of the main effects of batter and temperature and their
interaction. If an interaction exists, use a profile plot to interpret the
interaction. If no interaction exists, then calculate main effect means for each
factor.
c) Examine a residual by predicted plot and a normal plot of the residuals to
assess model assumptions.
2. Recent coverage of different cuisines has spurred an interest in doing a
taste test of foods from several countries. There is interest in comparing these
cuisines: American, Chinese, Ethiopian, Indian, Italian, Japanese, and
Vietnamese. The portion size dictates that subjects can only eat three food
samples. Find a balanced incomplete block design that satisfies these
objectives, and list for each block which cuisines will be sampled in that
block. You do not need to randomize the design.
3. A large restaurant chain chooses 4 towns, where each town has three of their
restaurants. In each of the 4 towns, the three restaurants are randomized to
either i) no change of employee uniform (light brown), ii) change to blue
uniform, or iii) light red uniform. Also, after the uniform changes took effect,
each restaurant implemented a soft-drink refill policy in a random order,
between i) i) free refills in store or ii) free refill all day with receipt.
Each drink refill treatment was used for 3 weeks. A single average daily sale
amount was calculated for each store for both drink settings from the last two
weeks for their 3 week periods, to allow a week for consumers to become aware of
the policies (in other words, each restaurant contributes two numbers, the
average daily sales reported separately for the two refill treatments).
a) Name this design and write the model equation.
b) Fill out a skeleton ANOVA table with the source and degree of freedom
columns.
4. A followup cuisine study wants to study desserts from these six cuisines:
Brazilian, Mexican, Persian, Russian, Swedish, and Thai. A colleague suggests
the following design that requires 6 subjects, each eating samples from four
cuisines: [(B,M,P,R), (M,P,R,S), (P,R,S,T), (R,S,T,B), (S,T,B,M), (T,B,M,P)].
Does each treatment have the same number of replicates? Is
this design a balanced incomplete block design? Explain your answer.