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# 10_19_09 - “Reject H if x< 28.6” b Suppose the...

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STAT 409 Examples for 10/19/2009 Fall 2009 H 0 true H 0 is NOT true Do Not Reject H 0 Type II Error Reject H 0 Type I Error α = significance level = P ( Type I Error ) = P ( Reject H 0 | H 0 is true ) β = P ( Type II Error ) = P ( Do Not Reject H 0 | H 0 is NOT true ) Power = 1 – P ( Type II Error ) = P ( Reject H 0 | H 0 is NOT true ) 1. A car manufacturer claims that, when driven at a speed of 50 miles per hour on a highway, the mileage of a certain model follows a normal distribution with mean μ 0 = 30 miles per gallon and standard deviation σ = 4 miles per gallon. A consumer advocate thinks that the manufacturer is overestimating average mileage. The advocate decides to test the null hypothesis H 0 : μ = 30 against the alternative hypothesis H 1 : μ < 30. a) Suppose the consumer advocate tests a sample of n = 25 cars. What is the significance level associated with the rejection region

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Unformatted text preview: “Reject H if x < 28.6” ? b) Suppose the consumer advocate tests a sample of n = 25 cars. Find the “best” rejection region with the significance level α = 0.05. c) Suppose the consumer advocate tests a sample of n = 25 cars and uses a 5% level of significance. Find the power of the test if the true mean is μ 1 = 29.5. d) Repeat part (c) for the case when the true value of the mean is μ 1 = 28.5. e) Repeat parts (c) and (d) using a larger sample size of n = 49. f) Repeat parts (c) and (d) using a 10% level of significance. g) What is the minimum sample size required if we want to have the power of at least 0.80 at μ 1 = 29.5 for the test with a 5% level of significance?...
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• Spring '11
• Stepanov
• Null hypothesis, Statistical hypothesis testing, Type I and type II errors, Statistical power, Consumer Advocate

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