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Week 10 Practice Problems
These problems involve tests of significance that make use of the central limit theorem
and the likelihood ratio.
1.
Suppose
2
1
~
W
χ
and
. Explain why
~(
0
,
1
)
ZG
()
(


PW d
P Z
d
≥=
≥
)
[we will use
this result below]
2.
In assessing a new treatment, 200 patients are tested and the treatment is successful
134 times. The standard treatment has a success rate of 60%. Is there any evidence
that the new treatment has a different success rate? Assume a binomial model is
appropriate.
a)
Carry out a test of significance using an approximation based on the central
limit theorem.
b)
Carry out a likelihood ratio test. Use the result in question 1 to get a good
approximation to the pvalue.
c)
How do the conclusions of the two tests compare?
3.
The number of flaws in a glass sheet can be modeled by a Poisson random variable.
Suppose a change is proposed to the production process. To see if the change affects
the number of flaws, a experiment is carried out. Twenty sheets of glass are produced
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 Spring '10
 McKay
 Central Limit Theorem

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