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ECON 206
1
Middle East Technical University
20102011 Fall
Department of Economics
ECON 206
Instructor: Ozan ERUYGUR
Research Assistant: Pelin AKÇAGÜN
PROBLEM SET 05
HYPOTHESIS TESTING
PROBLEM 1
The hourly wages in a particular industry are normally distributed with mean $ 13.20
and standard deviation $ 2.50. A company in this industry employs 40 workers,
paying them an average of $ 12.20 per hour. Can this company be accused of paying
substandard wages? Use an
.01
level test.
PROBLEM 2
The output voltage for a certain electric circuit is specified to be 130. A sample of 40
independent readings on the voltage for this circuit gave a sample mean of 128.6 and
a standard deviation of 2.1. Test the hypothesis that the average output voltage is 130
against the alternative that it is less than 130. Use a test with level .05.
PROBLEM 3
The Rockwell hardness index for steel is determined by pressing a diamond point into
the steel and measuring the depth of penetration. For 50 specimens of a certain type of
steel, the Rockwell hardness index averaged 62 with standard deviation 8. The
manufacturer claims that this type of steel has an average hardness index of at least
64. Is there sufficient evidence to refute the manufacturer's claim at the 1 %
significance level?
PROBLEM 4
Shear strength measurements derived from unconfined compression tests for two
types of soils gave the results shown in the following table (measurements in tons per
square foot).
Soil Type I
Soil Type II
1
1
1
30
1.65
0.26
n
y
s
2
2
2
35
1.43
0.22
n
y
s
Do the soils appear to differ with respect to avenge shear strength, at the 1 %
significance level?
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2
PROBLEM 5
The administrators for a hospital wished to estimate the average number of days
required for inpatient treatment of patients between the ages of 25 and 34. A random
sample of 500 hospital patients between these ages produced a mean and standard
deviation equal to 5.4 and 3.1 days, respectively. A federal regulatory agency
hypothesizes that the average length of stay is in excess of 5 days. Do the data support
this hypothesis? Use a
.05
PROBLEM 6
Refer to Problem 2. If the voltage falls as low as 128, serious consequences may
result. For testing
0
:
130
H
versus
:
128
a
H
, find the probability
of a type II
error for the rejection region used in Problem 2.
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This note was uploaded on 03/22/2012 for the course ECON 106 taught by Professor Kücüksenel during the Spring '12 term at Middle East Technical University.
 Spring '12
 Kücüksenel
 Economics

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