Stat 415 HW 6
10.2
The test statistic Y has a binomial distribution with n=20 and p
a A type I error occurs if the experimenter concluded that the drug dosage level induces sleep in less
that
80%
of the people suffering form insomnia when, in fact, drug dosage level does induce sleep in
80%
of insomnia.
b
α
=
P
(
reject
H
0

H
0
true
) =
P
(
Y
≤
12

p
= 0
.
8)
=0.32  use table 1 Appendix III.
c A type II error would occur if the experimenter concluded that the drug dosage level induces sleep in
80%
of the people suffering from insomnia when in fact fewer than
80%
experience relief.
10.3 a
whin
n
= 20
and
p
= 0
.
8
, it is necessary to find c such that
α
=
P
(
Y
≤
c

p
= 0
.
8) = 0
.
1
. From
table 1, Appendix III, this value is c=11.
10.7
a
H
0
:
μ
= 900
,
H
a
:
μ
6
= 900
b The rejection region with
α
= 0
.
1
is determined by a critical value of z such that
P
[

Z

> z
0
] = 0
.
1
This value is
z
0
= 2
.
58
and the rejection region is
R
=
{
z
:

z

>
2
.
58
}
c
Z
=
¯
y

μ
σ/
√
n
≈
¯
y

μ
s/
√
n
=

1
.
77
by the law of large numbers
d The observed value,
z
=

1
.
77
does not fall in the rejection region, and
H
0
is not rejected. We cannot
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 Spring '08
 YUZHANG
 Statistics, Binomial, Statistical hypothesis testing, Type I and type II errors, rejection region, drug dosage level

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