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 5.0. Suppose the population standard deviation is believed to be 0.43 seconds. We
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