Statistics 106
Homework 3 Solution
Due : Oct. 22, 2018, In Class
16.26
Refer to
Rehabilitation therapy
Problem 16.9.
Obtain the power of the test in Problem 16.9(e) if
μ
1
=
37,
μ
2
=
35 and
μ
3
=
28. Assume that
σ
=
4
.
5.
17.1
A student, asked to give a class demonstration of the use of a confidence interval for comparing two
treatment means, proposed to construct a 99 percent confidence interval for the pairwise comparison
D
=
μ
5

μ
3
, where there are a total of five factor levels. The student selected this particular comparison
because the estimated treatment means
¯
Y
5
.
and
¯
Y
3
.
are the largest and smallest, respectively, and stated:
“This confidence interval is particularly useful. If it does not contain zero, it indicates, with significance
level
α
=
.
01, that the factor level means are not equal.”
a. Explain why the student’s assertion is not correct.
b. How should the confidence interval be constructed so that the assertion can be made with significance
level
α
=
.
01?
Solution:
1
a type I error. The student made a comparison that was suggested by the data (finding the largest dif
ference between treatment sample means) such that the correct confidence interval should be wider