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.