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Unformatted text preview: STAT 409 Examples for 10/19/2009 Fall 2009 H true H is NOT true Do Not Reject H ☺ Type II Error Reject H Type I Error ☺ α = significance level = P ( Type I Error ) = P ( Reject H | H is true ) β = P ( Type II Error ) = P ( Do Not Reject H | H is NOT true ) Power = 1 – P ( Type II Error ) = P ( Reject H | H 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 = 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 : 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 “Reject H if x < 28.6” ?...
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- Spring '11
- Normal Distribution, Statistical hypothesis testing, Type I and type II errors, rejection region, Consumer Advocate