zFormula_CIHT

zFormula_CIHT - Formula Sheet Parameter Assumptions...

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Unformatted text preview: Formula Sheet Parameter Assumptions Normality known Normality unknown No normality known n large No normality unknown n large Normality 1 2 1; 2 Con...dence interval X X z t =2 pn s =2 pn H0 = = Test statistic z= t= X p n 0 0 X s p n 0 0 X z =2 pn = 0 z= X p n 0 X z s =2 pn = q 0 z= X s p n 0 known 2 2 2 X1 X1 X2 X2 z =2 2 1 n1 + 2 2 1 2 n2 = D0 1 2 z= Normality 1 2 2 1 = = unknown t =2 sp No normality 1 2 1; 2 q X1 X2 D0 r 2 2 1+ 2 n1 n2 1 n1 + 1 n2 = D0 1 2 t= X1 X2 D0 q 1 1 sp n + n 1 2 known X1 X2 z =2 n1 ; n2 large No normality 1 2 1; 2 q q 2 1 n1 + 2 2 n2 = D0 z= X1 X2 D0 r 2 2 1+ 2 n1 n2 unknown X1 p ^ p1 ^ p1 ^ z X2 q z pq ^^ n =2 s2 1 n1 + s2 2 n2 1 2 n1 ; n2 large p p1 p1 p2 p2 n large n1 ; n2 large n1 ; n2 large (n1 1)s2 +(n2 1)s2 1 2 n1 +n2 2 =2 = D0 p = p0 z= X1 X2 D0 r 2 s2 1 + s2 n1 n2 p2 ^ p2 ^ z z =2 q p p0 ^ z = p p0 q0 n p1 q1 ^ ^ n1 p1 q1 ^ ^ n1 + + p2 q2 ^ ^ n2 p2 q2 ^ ^ n2 p1 p= ^ p1 p2 = 0 X1 +X2 n1 +n2 z= z= p =2 q p2 p1 p2 ^ ^ q 1 pq n + n ^^ 1 1 2 = D0 6= 0 p ^ ^ q 1 p2 D0 p1 q1 ^ ^ p2 q ^ ^ + n 2 n 1 2 Note: s2 = p 1 ...
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