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Power and Type II error (One population
mean
)
Sec 8.6:
95,
97, 99
Supplementary
exercises
1
 Power and Type II error (One population
proportion
)
1. Let
p
denote the percentage that Arizona families open presents on Christmas Eve or
Christmas day. To test H
0
:
p
= 0.5 vs. H
a
:
p
> 0.5, 144 Arizona families were surveyed
and
x,
the number of families that open presents on Christmas Eve or Christmas day, was
observed.
(a) What is the rejection region for testing H
0
vs. H
a
at the 5% significance level?
(Answer: to the right of 0.5685)
(b) What is the power of this test when the true value of
p
is 0.65?
(0.9798)
(c) What is the probability of a Type II error when the true value of
p
is 0.6? (0.2206)
2. Let
p
denote the percentage of 1825 years old people who were users of marijuana in
1995. To test H
0
:
p
= 10% vs. H
a
:
p
> 10%, 100 people in that age group were randomly
selected, and
x,
the number of these who were current users of marijuana, was found.
(a) What is the rejection region for testing H
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 Winter '07
 Dan

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