Final Formulas

# Final Formulas - Formulas for Final Exam • Creating a...

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Unformatted text preview: Formulas for Final Exam • Creating a condence interval for µ, the margin of error is tα/2 (n−1) s √ n . • Testing for a population mean: ¯ X − µ0 √ ∼ t(n−1) s/ n • Testing for the dierence between two means in independent samples: ¯ ¯ (X1 − X2 ) − D0 s2 1 n1 + s2 2 n2 ∼ t(min{n1 −1, n2 −1}) • Testing for the dierence between two means in paired samples: ¯ d − µd √ ∼ t(n−1) sd / n • Testing for whether two categorical variables are independent: i j r i cj (fij − eij )2 ∼ χ2I −1)(J −1) where fij = ( eij n 1 • Correlation: rXY = n sXY 1 where sXY = (xi − x)(yi − y ) ¯ ¯ sX sy n − 1 i=1 • Regression: (xi − x)(yi − y ) ¯ ¯ sY = rXY 2 (xi − x) ¯ sX = y − b1 x ¯ ¯ SSE = (rXY )2 where SSE = = 1− SST b1 = b0 r2 (yi − yi )2 and SST = ˆ • Regression standard error s 1 SSE n−2 = • Condence interval for µY at x0 : (x0 − x)2 ¯ 1 + n (xi − x)2 ¯ (n−2) y ± tα/2 s ˆ • Prediction interval for Y at x0 : (n−2) y ± tα/2 s ˆ 1+ 2 1 (x0 − x)2 ¯ + (xi − x)2 ¯ n (yi − y )2 ¯ ...
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Final Formulas - Formulas for Final Exam • Creating a...

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