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04_04 - that the true average number of seconds it takes to...

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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. 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
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Unformatted text preview: 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 wish to test H : μ ≤ 5.0 vs. H 1 : μ > 5.0. Find the power of this test if the true average time is 5.15 seconds, a 5% level of significance will be used, and 50 automobiles will be tested (each automobile to be tested a single time). 3. Suppose n = 49 observations are taken from a normal distribution where σ = 8.0 for the purpose of testing H : μ = 60 versus H 1 : μ ≠ 60 at the α = 0.05 level of significance. What is the power of the appropriate test when μ = 59.2?...
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