04_04ans - STAT 410 Examples for Spring 2008 1 A car...

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STAT 410 Examples for 04/04/2008 Spring 2008 1. A car manufacturer claims that, when driven at a speed of 50 miles per hour, the miles-per-gallon rating of a certain model follows a normal distribution with mean 30 miles per gallon and standard deviation σ = 4 miles per gallon. A consumer advocate thinks that the manufacturer is overestimating average mileage. Suppose the consumer advocate tests a sample of n = 25 cars and uses a 5% level of significance. Find the power of the appropriate test if the true mean is μ 1 = 29.5. H 0 : μ = 30 vs. H 1 : μ < 30. Rejection Region : Z = n ± 0 X - < – z α . Z = 25 4 30 X - < 1.645. 25 4 645 . 1 30 X - < = 28.684 . Power = P ( X < 28.684 | μ 1 = 29.5 ) = ± ² ³ ³ ³ ³ ´ µ - < 25 4 5 . 29 684 . 28 Z P = P ( Z < – 1.02 ) = 0.1539 .
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2. An advertisement for a particular brand of automobile states that it accelerates from 0 to 60 mph in an average of 5.0 seconds. Makers of a competing automobile feel that the true average number of seconds it takes to reach 60 mph from zero is above
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This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

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04_04ans - STAT 410 Examples for Spring 2008 1 A car...

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