Statistics 106
Homework 6 Solution
Due : Feb. 17, 2016, In Class
19.5
In a two-factor study, the treatment means
μ
i j
are as follows:
Factor
B
Factor
A
B
1
B
2
B
3
B
4
A
1
250
265
268
269
A
2
288
273
270
269
a. Obtain the factor
B
main e
ff
ects. What do your results imply about factor
B
?
b. Prepare a treatment means plot and determine whether the two factors interact. How can you tell that
interactions are present? Are the interactions important or unimportant?
c. Make a logarithmic transformation of the
μ
i j
and plot the transformed values to explore whether this
transformation is helpful in reducing the interactions. What are your findings?
Solution:

b. The treatment means plot is shown below:
1

c. The transformed treatment means plot is shown below:
2

19.8
Refer to Problem 19.5. Assume that
σ
=
4 and
n
=
6.
a. Obtain
E
{
MS E
}
and
E
{
MS AB
}
.
b. Is
E
{
MS AB
}
substantially larger than
E
{
MS E
}
? What is the implication of this?
Solution:

3

19.12
Eye contact e
ff
ect.
In a study of the e
ff
ect of applicant’s eye contact (factor
A
) and personnel o
ffi
cer’s
gender (factor
B
) on the personnel o
ffi
cer’s assessment of likely job success of applicant, 10 male and
10 female personnel o
ffi
cers were shown a front view photograph of an applicant’s face and were asked
to give the person in the photograph a success rating on a scale of 0 (total failure) to 20 (outstanding
success). Half of the o
ffi
cers in each gender group were chosen at random to receive a version of the