04_02 - STAT 410 Examples for Spring 2008 Hypotheses Testing for the Population Mean Null Alternative vs vs vs H0 0 H0 0 H0 = 0 H1 < 0 H1 > 0 H1 0

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STAT 410 Examples for 04/02/2008 Spring 2008 Hypotheses Testing for the Population Mean μ Null Alternative H 0 : μ μ 0 vs. H 1 : μ < μ 0 Left - tailed. H 0 : μ μ 0 vs. H 1 : μ > μ 0 Right - tailed. H 0 : μ = μ 0 vs. H 1 : μ μ 0 Two - tailed. H 0 true H 0 false Accept H 0 ( 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 ) Test Statistic: n ± 0 X Z - = OR n s 0 ± X T - = OR X The P-value ( observed level of significance ) is the probability, computed assuming that H 0 is true, of obtaining a value of the test statistic as extreme as, or more extreme than, the observed value. (The smaller the p-value is, the stronger is evidence against H 0 provided by the data.) P-value > α Do Not Reject H 0 ( Accept H 0 ) . P-value < α Reject H 0 .
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2 Computing P-value. H 0 : μ μ 0 H 1 : μ < μ 0 Left - tailed. H 0 : μ μ 0 H 1 : μ > μ 0 Right - tailed. H 0 : μ = μ 0 H 1 : μ μ 0 Two - tailed. Area to the left of the observed test statistic Area to the right of the observed test statistic 2 × area of the tail Rejection Region: H 0 : μ μ 0 H 1 : μ < μ 0 Left - tailed. H
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This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

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04_02 - STAT 410 Examples for Spring 2008 Hypotheses Testing for the Population Mean Null Alternative vs vs vs H0 0 H0 0 H0 = 0 H1 < 0 H1 > 0 H1 0

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