STATISTICS 402 - Assignment 3
Due February 11, 2011
1. Chapter 4: Exercise Set A, pg 109, # 2 and 8.
Exercise Set B, pg 117, # 8 and 11.
Exercise Set C, pgs 124 – 125, # 2 and 3.
Exercise Set D, pgs 127 – 128, # 1, 2 and 3.
2. A biology department is interested in comparing students’ understanding of the frog’s
anatomy based on their experiences with dissection. They decide to look at three methods for
presenting the material. One method will have students dissect a real frog, another method
will have students use a computer program that simulates the dissection of a frog, and a third
method will have students spend half the time with a real frog and half the time with the
computer program. The dissection (real, virtual or both) will be conducted in the laboratory
section associated with the biology class. There are hundreds of these lab sections. The same
amount of time will be spent on dissection regardless of the dissection method (real, virtual or
both). At the end of the unit, all the students’ will take the same test on the anatomy of the
frog. There are two different ways to conduct the experiment. Experiment 1 – Select three
lab sections at random and assign one section, at random, to each of the methods. The
individual students’ test scores in each section will be analyzed. Experiment 2 – Select 15 lab
sections at random and assign 5 sections, at random, to each of the methods. The average test
score for each section will be analyzed.
a) What is the chance variation in each experiment? Describe in some detail the source of
this variation for each experiment.
b) Suppose the virtual dissection group had a statistically higher sample mean test score
when compared to the other two groups. What generalizations can be made for each
experiment?
3. A study will be performed to evaluate 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 member of the group using one of the hand
cleaning methods. After hands are cleaned the right hand of each volunteer will be placed on
a sterile media plate. Bacteria still on the hand will be transferred to the media that is
designed to facilitate bacterial growth. The plates are incubated for 2 days at 36o C. After
incubation the numbers of bacterial colonies are counted.
a) Explain briefly why this study is 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 the variable
controlled?
d) Give an example of an outside variable that is not controlled in the study? Explain
briefly.
e) There is not a control group in this study. How would you include a control group in this
study?
f) Is random selection used in this study? Explain briefly.
g) Suppose the experimenter wanted to be able to detect a one standard deviation difference
in group means with Alpha = 0.05 and Beta = 0.05, how many volunteers would be
needed for the experiment?
h) Only 36 people volunteer for the experiment. Give two combinations of Alpha, Beta and
the size of the detectable difference in group means that correspond to this number of
volunteer.
1
i)
j)
Describe in detail how you would randomly assign the volunteers to the three groups so
that there are an equal number of volunteers (12) in each group. Once you have described
what you will do, actually do the randomization. Include your randomized assignment of
the 36 volunteers to the 3 groups.
Is there replication within this study? Explain briefly.
4. A one factor, completely randomized experiment, as described in problem 1, is run. The
results appear on the next page.
a) Plot the data and compute summary statistics. If you use a computer program, cut and
paste the output on your answer sheet. 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, appropriate F statistic and associated P-value. If you use
a computer package, you can copy the results from the output onto your answer sheet. I
will not look at output simply attached at the end of what you turn in.
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 sample
mean counts of bacterial colonies? Support your answer by referring to the appropriate
test of the null hypothesis: H 0 :  1   2   3  0 .
f) Construct 95% confidence intervals for the differences in true mean numbers of bacterial
colonies for:
 Antibacterial Spray compared to Antibacterial Soap
 Antibacterial Spray compared to Regular Soap
 Antibacterial Soap compared to Regular Soap
g) Based on the confidence intervals in f), what pairs of treatments have differences in
sample means that are statistically significant?
h) Write a brief summary (one or two sentences is enough) of the findings of the
experiment. In this summary make a recommendation based on your analysis as to what
hand cleaning method should be used.
Data for Hand Cleaning Experiment
Mean, y
Variance, s 2
Antibacterial Spray
47
48
42
33
30
35
37
30
29
43
32
38
37.0
44.54
Antibacterial Soap
96
92
82
97
96
91
101
104
87
100
99
101
95.5
41.36
Regular Soap
107
106
89
91
108
94
100
101
97
99
100
108
100.0
42.00
2