Sta650 Fall 202: Statistical Foundation For Data Science

STA650 FALL 202: STATISTICALFOUNDATION FOR DATA SCIENCEConfidence Intervals Parameter Assumptions Endpoints N(, 2) or nlarge x z(/ 2) n 2is known N(, 2) x t(/ 2;n 1) s n 2is unknown 22( n 1) "(n 1)s2 2( / 2,n 1) ,(n 1)s2 2(1 / 2,n 1) # 1 2 Independent Normal distributions 21 , 22 are known x y z(/ 2)s 21 n1 +22 n2n 1, n2are large 1 2 Independent Normal distributions 21 , 22 are unknown x y t(/ 2;n1+n22) s (n1 1)s2x + (n2 1)s2y n1 +n2 2 1 n1 +1 n2but equal 21 / 22 Independent Normal distributionss21 s2 F(1 / 2;n11,n21) ,s21 s2 F(/ 2;n21,n11)p Binomialb(n, p ) y nz(/ 2)r (y/n )(1y/n ) nn is largep 1 p2 Independent BinomialX b(n1, p1),Y b(n2, p2) x n1y n2z(/ 2)s (x/n1)(1x/n1) n1 +(y/n2)(1y/n2) n2n 1, n2large1Test of HypothesesHypotheses Rejection Region of H0H 0: = 0 x 0 / nz( )H a: > 0H 0: = 0 x 0 s/ nt( ;n 1)H a: > 0H 0: 2= 20 (n 1)s2 20 2( ;n 1)H a: 2> 20H 0:1 =2 x y q21 n1 + 22 n2 z( )H a:1 > 2H 0:1 =2 x y r(n11)