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Formulas for the Final Exam y y=∑ ∑ ( y − y )2 ∑ ( x − x )2 x x=∑ sy = sx = n n −1 n n −1 ∑ zxz y z = x − x z = y − y r= x y n −1 sx sy sy b=r a = y − bx yˆ = a + bx residual = y − yˆ sx Sampling Distribution of p̂ : Sampling Distribution of y : Mean: p Mean: μ Standard Deviation: SD( pˆ ) = p(1 − p ) n Standard Error: SE( y ) = Single sample (Categorical Variable) Confidence interval for p : pˆ − z * pˆ (1 − pˆ ) to pˆ + z * n pˆ (1 − pˆ ) n pˆ − po p0 (1 − p0 ) n z= Test Statistic: s s to y + t * n n t= y − μo s n Two independent samples Confidence interval for μ1 − μ2 : ( y1 − y2 ) − t * df = n – 1 Test Statistic: s12 s22 s2 s2 + to ( y1 − y2 ) − t * 1 + 2 n1 n2 n1 n2 Paired samples Confidence interval for μd : s s d − t * d to d + t * d nd nd n Test Statistic: Single sample (Numerical Variable) Confidence interval for μ: y − t* s t= ( y1 − y2 ) − 0 s12 s22 + n1 n2 Test Statistic: t= d − μd sd nd df = nd – 1 1