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Unformatted text preview: Terminology : • the significance level of the test : an upper bound on the probability of type 1 error. It is also often denoted by α . • typical values of the significance level: 0 . 1 , . 05 , . 01 , . 005. • The significance level of the test is also called the size of the test. • For a simple null hypothesis H we choose the critical region so that α = probability of type 1 error = significance level = α. • For a composite null hypothesis H we choose the critical region so that α ( θ ) = P (reject H  the true parameter is θ ∈ Ω ) ≤ significance level = α. • The critical region of a test with signifi cance level α is called a size α critical re gion. The power function of a test : η ( θ ) = 1 β ( θ ) = P (reject H  the true parameter is θ ∈ Ω 1 ) . Among alternative tests with a given signifi cance level α , the one with a higher power is better. Constructing powerful tests using likelihood ratios Testing simple hypothesis • We need to test a simple hypothesis against a simple alternative H : θ = θ vs. H 1 : θ = θ 1 at a significance level α . •...
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 Fall '09
 SAMORODNITSKY
 Null hypothesis, Hypothesis testing, Statistical hypothesis testing, probability density function, Type I and type II errors, significance level

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