Problem%20Set%2002_2010_2011[1]

# Problem%20Set%2002_2010_2011[1] - Middle East Technical...

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Middle East Technical University 2010-2011 Fall Department of Economics ECON 206 Instructor: Ozan ERUYGUR Research Assistant: Pelin AKÇAGÜN PROBLEM SET 02 SAMPLING DISTRIBUTIONS PROBLEM 1 Refer to Example 7.1; the amount of fill dispensed by a bottling machine is normally distributed with σ = 1 ounce. If = 9 bottles are randomly selected from the output of the machine, we found that the probability that the sample mean will be within .3 ounce of the true mean is .6318. Suppose that n Y is to be computed using a sample of size . n a) If n = 16, what is () .3 PY μ −≤ ? b) Find ( .3 ) when Y is to be computed using samples of sizes n n n n = 25, = 36, = 49, = 64. c) What pattern do you observe among the values for ( ) .3 that you observed for the various values of ? n d) Do the results that you obtained in part (b) seem to be consistent with the result obtained in Example 7.2? PROBLEM 2 Refer to Problem 1. Assume now that the amount of fill dispensed by the bottling machine is normally distributed with = 2 ounce. a) If n = 9 bottles are randomly selected from the output of the machine, what is ( .3 ) ? Compare this with the answer obtained in Example 7.1. b) Find ( .3 ) when Y is to be computed using samples of sizes n n n n = 25, = 36, = 49, = 64. ECON 206 1

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c) What pattern do you observe among the values for ( ) .3 PY μ −≤ that you observed for the various values of ? n d) How do the respective probabilities obtained in this problem (where σ = 2) compare to those obtained in Exercise 7.1 (where
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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%20Set%2002_2010_2011[1] - Middle East Technical...

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