Problem Set 05_2010_2011 - Middle East Technical University...

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ECON 206 1 Middle East Technical University 2010-2011 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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ECON 206 2 PROBLEM 5 The administrators for a hospital wished to estimate the average number of days required for in-patient 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.

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Problem Set 05_2010_2011 - Middle East Technical University...

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