Up:
Stat 5132
Problem 1
Assume
X
1
,
,
X
20
are i. i. d.
.The observed value of
is 23.6. Perform a one-tailed test
of the hypotheses
versus
,finding the
P
-value.
Problem 2
Two groups in physics lab have been measuring the density of aluminum at room temperature (
C).
They got the following summary statistics
n
S
n
Group I
10
2.792
0.241
Group II
8
2.538
0.313
(Units are grams per cubic centimeter.) Assume the measurements for group I are i. i. d.
and
the measurements for group II are i. i. d.
.We want to perform a test of
versus
.Perform Welch's approximate test, come as close as you can to the
P
-value.
Problem 3
We intend to collect a series of i. i. d. measurements and conduct a test of
versus
,where
is the expected value of the measurements. The sample size will be large
enough so that we can use the ``large sample''
z
-test. Preliminary studies suggest that the standard
deviation of the measurements is about 4. What sample size do we need to have power 0.90 at
for a test of size
?

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