STATISTICS 402 – Assignment 10
Due April 27, 2009
1. What is a picnic without ants? A student in a statistics class in Australia designed
an experiment to see if different types of sandwiches attract different numbers of
meat ants (a scavenger ant found throughout Australia). The results were reported
by Margaret Mackasack (1994), “Favourite Experiments: An Addendum to What
is the Use of Experiments Conducted by Statistics Students?” in the Journal of
Statistics Education, v2n1. The experiment involved different combinations of
bread, filling and butter to make a sandwich. The sandwich was then left next to a
meat ant hill. After 5 minutes the experimenter counted the number of ants within
a specified radius of the sandwich. The factors of interest were; type of bread (rye,
whole meal, multi-grain, or white); the type of filling (Vegemite, Peanut Butter or
Ham and Pickle, and whether butter was put on the bread (yes or no). Two
sandwiches were made for each combination and the order in which sandwiches
were placed near the meat ant hill was completely randomized. Each sandwich
was cleaned up and the ants were allowed to return to the hill before placing
another sandwich. Below are the data.
Filling
Vegemite Peanut Butter Ham and Pickle
Bread Butter Yes No Yes No Yes No
22 18 27 43 68 44
Rye 45 31 50 36 65 54
57 29 42 59 58 34
Whole meal 42 21 36 47 77 65
26 42 60 22 63 36
Multi-grain 28 38 47 19 76 59
52 42 57 24 66 48
White 40 25 51 21 59 53
a. Use the sample size tables from earlier in the semester to determine the size of
the difference in mean quality that can be detected when comparing the:
• Two levels of butter.
• Three levels of filling.
• Four levels of bread.
For all determinations use Alpha=0.05 and Beta=0.10.
b. Construct a complete ANOVA table (you can, and should, use JMP to do the
calculations).
c. What factors and/or interactions are statistically significant at the 1% level?
d. Compute means for those factors that are statistically significant. Indicate
which means are significantly different for the significant factors. Be sure to
include the value of the LSD or HSD used.
e. Compute means for the significant interactions. Construct and interpret
interaction plots for the significant interactions.
f. Based on your analysis, what sandwich attracts the most meat ants? The
fewest meat ants? Support your answer statistically.
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