STATISTICS 402 - Assignment 3
Due February 17, 2006
1. An experiment is performed to see the effectiveness of different hand cleaning methods on
eliminating bacteria from hands. There are three hand cleaning methods: 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 36 o C. 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 0.8
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. Include the your randomized
assignment of the 33 volunteers to the 3 groups.
2. The experiment described in problem 1 is run with the following results.
1. Antibacterial
Spray
47
48
42
33
30
35
30
29
43
32
38
2. Antibacterial
Soap
96
92
82
97
96
91
104
87
100
99
101
Regular
Soap
107
106
89
91
108
94
101
97
99
100
108
Mean, Y i
37.0
95.0
100.0
Variance, s2i
49.0
42.2
46.2
1
(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?
(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.
(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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