exam1-formulas - Useful Formulas n expected value = xi P...

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expected value = n X i =1 x i P ( x i ) s = v u u t 1 n - 1 n X i =1 ( x i - ¯ x ) 2 Probability P ( A B ) = P ( A ) + P ( B ) - P ( A B ) P ( A | B ) = P ( A B ) P ( B ) P ( X = x ) = ± n x ² p x (1 - p ) n - x mean = np standard deviation = np (1 - p ) Statistical Inference test statistic = estimator - null value standard error estimator ± (confidence #)(standard error) z = ˆ p - p 0 q p 0 (1 - p 0 ) n ˆ p ± z 1 - α/ 2 r ˆ p (1 - ˆ p ) n t = ¯ x - μ s/ n ¯ x ± t 1 - α/ 2 s n t Distribution Table Confidence Level 80% 90% 95% 98% 99% 99.8% Right-Tail Probability df 0.100 0.050 0.025 0.010 0.005 0.001 1 3.078 6.314 12.706 31.821 63.657 318.309 2 1.886 2.920 4.303 6.965 9.925 22.327 3 1.638 2.353 3.182 4.541 5.841 10.215 4 1.533 2.132 2.776 3.747 4.604 7.173 5 1.476 2.015 2.571 3.365 4.032 5.893 6 1.440 1.943 2.447 3.143 3.707 5.208 7 1.415 1.895 2.365 2.998 3.499 4.785 8 1.397 1.860 2.306 2.896 3.355 4.501 9 1.383 1.833 2.262 2.821 3.250 4.297 10 1.372 1.812
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exam1-formulas - Useful Formulas n expected value = xi P...

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