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

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

Statistics and Data Analysis Part 22 – Statistical Tests: 1

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

Power of the Test of a Mean Rejection region. Probability = 0.025 29745.2 30,000 30254.2 Rejection region. Probability = 0.025 36/42

Power Against a Specific Alternative 37/42

Power Function for the test of μ = \$30,000 Alternative Power of Test \$29,600.87 \$29,650.77 \$29,700.64 \$29,750.49 \$29,800.34 \$29,850.21 \$29,900.12 \$29,950.07 \$30,000.05 \$30,050.07 \$30,100.12 \$30,150.21 \$30,200.34 \$30,250.49 \$30,300.64 \$30,350.77 \$30,400.87 38/42

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