(HW_6_1) A study was conducted to compare the effectiveness
of two brands of fly spray as fly repellents. 18 boards were coated
in honey. The ends of 9 were sprayed with brand A and the other 9
sprayed with brand B. One of each type of board was used under each
of nine different environmental conditions. (It is known that the fly populations
differ, depending on environment.) For each board, the number of flies that
landed on it during a 30 minute period was recorded. The resulting data is
as follows:
Environment:
1
2
3
4
5
6
7
8
9
Mean
Standard Deviation
Brand A:
23
17
28
48
10
36
15
22
94
32.56
___
Brand B:
36
22
25
60
16
34
28
22
104
38.56
___
Difference:
_
_
_
_
_
_
_
_
_
___
Complete the table.
In this question you will perform 2 different types of analyses
on the above data. Both of these tests may not be appropriate; you
will discuss this issue in part (c). For the two tests please clearly state
your hypotheses, show your work to get the statistics and
interpret the results.
Treating the data as from two independent samples (with the
brand A data as sample 1 and the brand B data as sample 2),
carry out a 2-sided t-test to investigate whether there is a difference between
the two brands in the average numbers of flies landing on the boards.
Treating the data as paired, carry out a 2-sided t-test to investigate
whether there is a difference between the two brands in the average numbers
of flies landing on the boards.
Should we treat the data as from two independents samples
or from paired data? Briefly justify your answer. Draw an appropriate dotplot
for this dataset. Which of the tests from part (b) is most appropriate for
this data? Justify your answer.
(HW_6_2) An advertisement for Seldane-D, a
drug prescribed for seasonal allergic hay fever, reported the results of
a double blinded study in which 374 patients took Seldane-D
and 193 took a placebo, (Time, March 27, 1995, p. 18). Headaches
were reported as a side effect by 65 taking the drug and by 43 taking the
placebo. Address in a statistical manner the hypothesis that the between group difference in the
proportions of patients reporting headaches are significant.
(HW_6_3) A quality control officer of a large metal pin
manufacturer wants to assess the breaking strength of more cost efficient
alloy pins and see if the new alloy material will meet the spec requirements
for the pins. A random sample of 5 alloy pins is taken and their breaking
strengths obtained in psi units, {42,110; 42,550; 41,895; 42,285,
41,990}. What is your recommendation on whether we should adopt the new (cost
effective) alloy manufacturing process, assuming the required breaking strength
of the pins should be 42,300 psi.
\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology,
UCLA School of Medicine/