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Statistics and Data Analysis Professor William Greene Stern School of Business IOMS Department Department of Economics

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Statistics and Data Analysis Part 22 – Statistical Tests: 1

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The Power of a Test Procedure Power = The probability it will correctly reject a false hypothesis. A type II error occurs when you fail to reject a false hypothesis. β = probability of a type II error. (Standard notation in statistics – yes, it does conflict with the standard notation for regression coefficients.) Power = 1 – β Power depends on what the true value is (remember, the null is false, so something else is true). 35/42

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Power of the Test of a Mean Rejection region. Probability = , Rejection region. Probability = /42

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Power Against a Specific Alternative 37/42

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Power Function for the test of μ = $30,000 Alternative Power of Test $29, $29, $29, $29, $29, $29, $29, $29, $30, $30, $30, $30, $30, $30, $30, $30, $30, /42

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