Homework Chapters 1 through 6, due Tuesday, October 5, 2010. The first seven
problems are like examination problems. The last three problems are from your text.
1.
A research team takes a random sample of size 25 from the random variable
Y
,
which is
)
100
,
(
2
μ
N
. They observe that
541
25
=
y
. Test the null hypothesis that
500
)
(
:
0
=
Y
E
H
against the alternative
500
)
(
:
1
≠
Y
E
H
at the 0.10, 0.05, and
0.01 levels of significance. Calculate the 95% confidence interval for
μ
.
2.
A research team wishes to test the null hypothesis that a dependent variable
Y
has
500
)
(
=
Y
E
with standard deviation 100 at the 0.01 level of significance against
the alternative that
500
)
(
Y
E
. They want the probability of a Type II error to be
0.01 when
550
)
(
=
Y
E
with standard deviation 100. How many independent
observations
n
are needed?
3.
A research team takes a sample of 8 observations from the random variable
Y
,
which has a normal distribution
)
,
(
2
σ
μ
N
. They observe
2
.
563
8
=
y
, where
8
y
is
the average of the eight sampled observations and
2
.
453
2
=
s
is the observed
value of the unbiased estimate of
2
σ
, based on the sample values. Test the null
hypothesis that
600
)
(
:
0
=
Y
E
H
against the alternative
600
)
(
:
1
≠
Y
E
H
at the
0.10, 0.05, and 0.01 levels of significance.
4.
A research team took a random sample of 8 observations from a normally
distributed random variable
Y
and observed that
8
.
64
8
=
y
and
2
.
12
2
=
Y
s
, where
8
y
is the average of the eight observations sampled from
Y
and
2
Y
s
is the unbiased
estimate of
)
var(
Y
. A second research team took a random sample of 6
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 Fall '08
 Staff
 Normal Distribution, Standard Deviation, research team

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