tests4means

tests4means - Summary of the Risk in Decision Making Actual...

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Unformatted text preview: Summary of the Risk in Decision Making Actual Situation Statistical Decision Do not reject H0 H0 True Correct decision Probability = 1 – α, the confidence level Type I error Probability = α, the significance level H0 False Type II error Probability = β Correct decision Probability = 1 – β , the power Reject H0 Summary of Significance Tests for the Mean of a Normal Population A. n large: σ known * Null Hypothesis, H0 µ = µ 0 or µ ≤ µ 0 Alternative Hypothesis, Ha or H1 µ > µ0 Test Statistic Decision Rule Reject H0 if z > zα Reject H0 if z < –zα z= z= z= x − µ0 µ = µ 0 or µ ≥µ 0 µ = µ0 µ < µ0 µ ≠µ 0 σn x − µ0 σn x − µ0 σ n z > zα 2 Reject H0 if or z < − zα 2 * If σ unknown, use s to estimate σ. B. n small: normal population and σ unknown Null Hypothesis, H0 µ = µ 0 or µ ≤ µ 0 Alternative Hypothesis, Ha or H1 µ > µ0 Test Statistic Decision Rule Reject H0 if t > tn-1,a t= t= t= x − µ0 sn x − µ0 sn x − µ0 s n µ = µ 0 or µ ≥µ 0 µ = µ0 µ < µ0 µ ≠µ 0 Reject H0 if t < –tn-1,α t > t n − 1, α 2 Reject H0 if or t < −t n −1,α 2 © 1999 by Harvey A. Singer © 1999 by Harvey A. Singer ...
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tests4means - Summary of the Risk in Decision Making Actual...

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