AMS 315
Data Analysis
Fall Semester, 2010
Chapter Seven Homework
Assignment due on Tuesday, October 12, 2010
1.
A research team takes a sample of 10 observations from the random variable
Y
, which has
a normal distribution
)
,
(
2
σ
μ
N
. They observe
2
.
343
10
=
y
, where
10
y
is the average of
the ten sampled observations, and
2
.
415
2
=
s
, where
2
s
is the observed value of the
unbiased estimate of
2
, based on the sample values. Test the null hypothesis that
300
:
2
0
=
H
against the alternative
300
:
2
1
H
at the 0.01 level of significance.
What is the 95% confidence interval for
2
? Note that an examination question would
either ask for the test or the confidence interval.
2.
A research team takes a sample of 8 observations from the random variable
Y
, which has
a normal distribution
)
,
(
2
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
, based on the sample values. Test the null hypothesis that
144
:
2
0
=
H
against the alternative
144
:
2
1
≠
H
at the 0.10, 0.05, and 0.01 levels of significance.
3.
A research team took a random sample of 15 observations from a normally distributed
random variable
Y
and observed that
1
.
17
15
=
y
and
7
.
36
2
=
Y
s
, where
15
y
is the average
of the fifteen sampled observations and
2
Y
s
is the unbiased estimate of
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 Fall '08
 Staff
 Normal Distribution, Standard Deviation, Variance, Student's tdistribution

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