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Unformatted text preview: ECO 230 Marianna Kudlyak Economic Statistics Spring 2007 Answer Key to Homework #9 Graded exercises: Exercise 1 (2 points),2 (2 points), 4 (2 points), and 5 (2 points). One point for the presence of each of the remaining 2 exercises. Exercise 1. Newbold, Carlson and Thorne, Problem 7.15 Exercsie 2. a) What is the sampling distribution of the sample mean? Provide the name of the distribution, its mean, and variance. Explain how you know that the distribution is as you specified. The distribution of the sample mean is normal with mean 295,100 and variance 74,000 2 /100. The distribution is normal because the sample size is large enough and the Central Limit Theorem can be applied. b) What is the probability that the sample mean price for new homes will be within $10,000 of the population mean? 82 . 1 ) 35 . 1 ( 2 )) 35 . 1 ( 1 ( ) 35 . 1 ( ) 35 . 1 ( ) 35 . 1 ( ) 35 . 1 35 . 1 ( ) 100 / 000 , 74 000 , 10 100 / 000 , 74 000 , 10 ( ) 000 , 10 000 , 10 ( ≅ − = − − = − − = < < − = − + < < − − = + < < − F F F F F Z P Z P X P µ µ µ µ µ µ c) What is the probability that the sample mean exceeds population mean by more than $20,000? 9965 . 1 ) 70 . 2 ( 1 ) 7 . 2 ( ) 100 / 000 , 74 000 , 20 ( ) 000 , 20 ( − ≅ − = > = − + > = + > F Z P Z P X P µ µ µ = 0.0035 d) The probability is 0.5 that the sample mean exceeds the population mean by how much? , . 100 / 000 , 74 5 . ) ( : 5 . ) 100 / 000 , 74 ( 5 . ) 100 / 000 , 74 ( 1 ) 100 / 000 , 74 ( ) 100 / 000 , 74 ( ) ( = = = = = = − = > = − + > = + > a Hence a Then z for z F table the From a F a F a Z P a Z P a X P µ µ µ The probability is 0.10 that the sample mean exceeds the population mean by how much? 472 , 9 7400 * 28 . 1 , . 28 . 1 100 / 000 , 74 28 . 1 9 . ) ( : 90 . ) 100 / 000 , 74 ( 10 . ) 100 / 000 , 74 ( 1 ) 100 / 000 , 74 ( ) 100 / 000 , 74 ( ) ( = = = = = = = − = > = − + > = + > a Hence a Then z for z F table the From a F a F a Z P a Z P a X P µ µ µ e) How large a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than $10,000 is less than 0.10? from the population mean by more than $10,000 is less than 0....
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This note was uploaded on 06/09/2008 for the course ECO 230 taught by Professor Kudlyak during the Spring '08 term at Rochester.
 Spring '08
 Kudlyak

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