STATISTICS 402 - Assignment 3
Due February 16, 2007
1. An experiment is performed to see the effectiveness of different hand cleaning
methods on eliminating bacteria from hands. The three hand cleaning methods
are: washing with soap, washing with antibacterial soap, and spraying with an
antibacterial spray (65% Ethanol). Volunteers will be assigned to groups with
each group using one of the hand cleaning methods. After hands are cleaned the
right hand of each volunteer is placed on a sterile media plate. Bacteria still on
the hand will be transferred to the media that is designed to encourage bacterial
growth. The plates are incubated for 2 days at 36oC. After incubation the number
of bacterial colonies are counted.
a) Why is this an experiment and not an observational study?
b) Identify the response, conditions and experimental units.
c) Give an example of an outside variable that is controlled in the study. How is
it controlled?
d) Give an example of an outside variable that is not controlled in the study?
Explain briefly.
e) If the experimenter wishes to detect a difference in mean bacterial counts as
small as 0.9 standard deviations with Alpha=0.05 and Beta=0.10, how many
volunteers are needed?
f) The experimenter is only able to recruit 33 volunteers. Give two combinations
of Alpha, Beta and ∆ σ that correspond to this number of volunteers. Briefly
explain the difference between the two choices.
g) Describe in detail how you would randomly assign the volunteers to the three
groups so that there are an equal number of volunteers in each group. Do the
randomization you describe. Include your randomized assignment of the 33
volunteers to the 3 groups.
2. The experiment described in problem 1 is run with the following results.
Mean
Variance
1. Antibacterial Spray
47
48
42
33
36
35
30
34
43
32
38
38.0
37.6
2. Antibacterial Soap
96
92
82
93
96
91
101
87
100
95
101
94.0
35.0
3. Regular Soap
103
104
89
91
105
94
101
97
99
100
106
99.0
32.4
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a) Plot the data. Based on the plot what can you say about the effectiveness of the
various methods? What can you say about the consistency of the methods?
Remember to tell me what you see in the plot and how that relates to the answers
to the questions.
b) Estimate the effect of each of the hand cleaning methods.
c) Construct an analysis of variance table giving sources of variation, degrees of
freedom, sums of squares, mean squares, the appropriate F statistic and
associated P-value.
d) Give the value of R2 and an interpretation of this value.
e) Are there statistically significant differences amongst the three groups in terms of
mean counts of bacterial colonies? Support your answer by referring to the
appropriate test of hypothesis. Include the null and alternative hypotheses, value
of the test statistic, P-value, decision and reason for reaching that decision.
f) If there are statistically significant differences, which groups are different?
Support your answer with a multiple comparisons method.
g) Look at the distribution of residuals. What does this tell you about the conditions
necessary for the analysis of variance? Be sure to tell me what you see and what
it means.
h) Write a brief summary (one or two sentences is enough) of the findings of the
experiment.
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