# 07_27 - STAT 410 Examples for Summer 2009 Hypotheses...

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STAT 410 Examples for 07/27/2009 Summer 2009 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 σ μ 0 X Z - = OR n s 0 μ 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 0 : μ μ 0 H 1 : μ > μ 0 Right - tailed. H 0 : μ = μ 0 H 1 : μ μ 0 Two - tailed.
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