Dr. V.R. Bencivenga
Economics 329
PRACTICE ASSIGNMENT #9B:
HYPOTHESIS TESTING I
For each problem, state the null and alternative hypotheses in terms of the parameter(s) of probability model
for the data, and give the test statistic; its sampling distribution; the reason why the sampling distribution is
valid; the rejection region; and the conclusion of the test.
1.
You are interested in the value of the mean of a normal population whose variance is known to be 100.
Consider testing the null hypothesis H
0
:
= 0 versus the alternative hypothesis H
A
:
= 2.
What is the
minimum sample size
needed to control the probability of Type I error at 5%, while simultaneously
controlling the probability of Type II error at 5%?
2.
A manufacturer of pharmaceuticals is concerned about the concentration of impurities in a drug.
The
standard is that the concentration of impurities should not exceed 2.5 percentage points in the
population of batches of the drug produced by this manufacturer.
It is known that in this population, the
distribution of impurity concentrations is approximately normal with standard deviation .3 percentage
point.
The null hypothesis is that the population mean impurity concentration is at most 2.5.
The
alternative hypothesis is that the population mean exceeds 2.5.
A random sample of nine batches will be
tested.
a.
What rejection region restricts the probability of Type I error to be at most 10%?
b.
What rejection region restricts the probability of Type I error to be at most 5%?
c.
If the population mean is 2.4, what is the probability of Type I error for the test in part b?
d.
If the population mean is 2.6, what is the power of the test in part b?
What is the probability of
Type II error?
e.
Graph the sampling distributions of the sample mean under the null hypothesis (specifically, for a
population mean of 2.5) and under the alternative hypothesis (specifically, for a population mean
of 2.6).
On your graph, represent the null and alternative hypotheses, the acceptance and
rejection regions from part b, and the probabilities of Type I and Type II error from parts b and d.
f.
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 Spring '12
 BENCIVENGA
 Economics

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