Formulas and Tables from Beginning Statistics

Transcription

1 Fmula ad Table from Begg Stattc Chater Cla Mdot Relatve Frequecy Chater 3 Samle Mea Poulato Mea Weghted Mea Rage Lower Lmt Uer Lmt Cla Frequecy Samle Se µ ( w) w f Mamum Data Value - Mmum Data Value Poulato Stadard Devato Samle Stadard Devato ( µ ) ( ) Poulato Coeffcet of Varato CV Samle Coeffcet of Varato Poulato Varace µ 00% CV 00% µ Samle Varace ( ) mrcal Rule f Bell-Shaed Dtrbuto Aromately 68% of the data value le wth oe tadard devato of the mea. Aromately 95% of the data value le wth two tadard devato of the mea. Aromately 99.7% of the data value le wth three tadard devato of the mea. Chebyhev Theem The roto of ay data et lyg wth K tadard devato of the mea at leat f K >. K Locato of Data Value f the P th Percetle P th Percetle of a Data Value l P 00 P l 00 Quartle Q Frt Quartle: 5% of the data are le tha equal to th value. Q Secod Quartle: 50% of the data are le tha equal to th value. Q 3 Thrd Quartle: 75% of the data are le tha equal to th value. Iterquartle Rage IQR Q Q Stadard Sce f a Poulato Stadard Sce f a Samle 3 µ Hawe Learg Sytem 04

2 Chater 4 ermetal Probablty ( mrcal Probablty) P( ) Clacal Probablty ( Theetcal Probablty) P( ) S f Comlemet Rule f Probablty P( ) P( c ) Addto Rule f Probablty P F P P F P ad F Addto Rule f Probablty of Mutually cluve vet P( F) P( ) P( F ) Multlcato Rule f Probablty of Ideedet vet P( ad F) P( ) P( F ) Multlcato Rule f Probablty of Deedet vet P ad F P P F P F P F Codtoal Probablty P ad F P( F ) P Secal Permutato!!!! Chater 5 ected Value ( X) µ P( X ) Varace f a Dcrete Probablty Dtrbuto P X µ ( µ ) P X Stadard Devato f a Dcrete Probablty Dtrbuto P X µ ( ) µ P X Probablty f a Bomal Dtrbuto P( X ) C ( ) Probablty f a Poo Dtrbuto e P( λ λ X )! Probablty f a Hyergeometrc Dtrbuto C C P( X ) C Fudametal Coutg Prcle The total umber of oble outcome f the equece of tage a multtage eermet. Factal Combato Permutato ( ) ()! C r P! r! r! r! r! Chater 6 Stadard Sce µ Fdg the Value of a mally Dtrbuted Radom Varable f a Gve Probablty µ mal Dtrbuto Aromato of a Bomal Dtrbuto µ Hawe Learg Sytem 04

3 Chater 7 The Cetral Lmt Theem (CLT). Mea of a Samlg Dtrbuto of Samle Mea µ µ. Stadard Devato of a Samlg Dtrbuto of Samle Mea 3. The hae of a amlg dtrbuto of amle mea wll aroach that of a mal dtrbuto, regardle of the hae of the oulato dtrbuto. The larger the amle e, the better the mal dtrbuto aromato wll be. Stadard Sce f a Samle Mea µ Poulato Proto Samle Proto µ Mea of a Samlg Dtrbuto of Samle Proto µ Stadard Devato of a Samlg Dtrbuto of Samle Proto Stadard Sce f a Samle Proto µ Chater 8 Marg of rr of a Cofdece Iterval f a Poulato Mea ( Kow) ( )( ) α α Cofdece Iterval f a Poulato Mea < µ < (, ) Mmum Samle Se f tmatg a Poulato Mea α Marg of rr of a Cofdece Iterval f a Poulato Mea ( Uow) ( t ) df wth α Marg of rr of a Cofdece Iterval f a Poulato Proto α Cofdece Iterval f a Poulato Proto < < (, ) Mmum Samle Se f tmatg a Poulato Proto α Cofdece Iterval f a Poulato Varace < < χ χ α ( α ) wth df Cofdece Iterval f a Poulato Stadard Devato < < χ χ α ( α ) wth df Hawe Learg Sytem 04

4 Chater 9 Marg of rr of a Cofdece Iterval f the Dfferece betwee Two Poulato Mea ( Kow) α Cofdece Iterval f the Dfferece betwee Two Poulato Mea ( ) < µ µ < ( ) (( ), ( ) ) Marg of rr of a Cofdece Iterval f the Dfferece betwee Two Poulato Mea ( Uow, Uequal Varace) tα wth df maller of the value ad Marg of rr of a Cofdece Iterval f the Dfferece betwee Two Poulato Mea ( Uow, qual Varace) t α Pared Dfferece ( ) wth df d Mea of Pared Dfferece d d Samle Stadard Devato of Pared Dfferece ( d d) d Marg of rr of a Cofdece Iterval f the Mea of the Pared Dfferece f Two Poulato ( Uow, Deedet Samle) d ( t ) df wth α Cofdece Iterval f the Mea of the Pared Dfferece f Two Poulato (Deedet Samle) d < µ < d ( d, d ) Marg of rr of a Cofdece Iterval f the Dfferece betwee Two Poulato Proto α d Cofdece Iterval f the Dfferece betwee Two Poulato Proto ( ) < < ( ) (( ), ( ) ) Pot tmate f Comarg Two Poulato Varace wth Cofdece Iterval f the Rato of Two Poulato Varace F < < α F( α ) wth df ad df Cofdece Iterval f the Rato of Two Poulato Stadard Devato F < < F α ( α ) wth df ad df Chater 0 Level of Sgfcace α c Tet Stattc f a Hyothe Tet f a Poulato Mea ( Kow) µ Hawe Learg Sytem 04

5 Tet Stattc f a Hyothe Tet f a Poulato Mea ( Uow) µ t wth df Tet Stattc f a Hyothe Tet f a Poulato Proto Tet Stattc f a Hyothe Tet f a Poulato Varace Poulato Stadard Devato ( ) χ wth df Tet Stattc f a Ch-Square Tet f Goode of Ft χ O wth df ected Value of a Frequecy a Cotgecy Table ( row total )( colum total ) Tet Stattc f a Ch-Square Tet f Aocato χ Chater O wth df ( R) C Tet Stattc f a Hyothe Tet F Two Poulato Mea ( Kow) ( )( µ µ ) Tet Stattc f a Hyothe Tet F Two Poulato Mea ( Uow, Uequal Varace) ( )( µ µ ) t wth df maller of the value ad Tet Stattc f a Hyothe Tet F Two Poulato Mea ( Uow, qual Varace) ( )( µ µ ) t ( ) ( ) wth df Tet Stattc f a Hyothe Tet f the Mea of the Pared Dfferece f Two Poulato ( Uow, Deedet Samle) d µ d t wth df d Tet Stattc f a Hyothe Tet f Two Poulato Proto ( )( ) ( ) Weghted tmate of the Commo Poulato Proto Tet Stattc f a Hyothe Tet f Two Poulato Varace F wth df df ad Grad Mea ( ) Sum of Square amog Treatmet (SST) SST Sum of Square f rr (SS) SS ( j ) ( j ) j Total Varato ( ) j j j ( j ) ( j ) j j j j SST SS Hawe Learg Sytem 04

6 Mea Square f Treatmet (MST) SST MST wth DFT DFT Mea Square f rr (MS) SS MS wth DF DF T Tet Stattc f a AOVA Tet MST F wth df DFT ad df DF T MS Chater Pearo Crelato Coeffcet r ( )( ) y y y y uch that r Tet Stattc f a Hyothe Tet f a Crelato Coeffcet t r r wth df Sloe of the Leat-Square Regreo Le b y y ( ) y-itercet of the Leat-Square Regreo Le b y b 0 Stadard rr of tmate ( y y ) Se SS Marg of rr f a Predcto Iterval f a Idvdual y-value 0 tα Se ( ) ( ) Predcto Iterval f a Idvdual y-value y < y < y ( y, y ) Multle Regreo Model y b b b b 0 Crtcal Value of Level of Cofdece, c α c α Regreo Le (Le of Bet Ft) y β0 β ( Poulato arameter) y b b ( Samle tattc) 0 Redual y y c α α α 0 α Sum of Squared rr (SS) ( ) SS y y Hawe Learg Sytem 04

7 A Stadard mal Dtrbuto umercal etre rereet the robablty that a tadard mal radom varable betwee - ad where µ Hawe Learg Sytem 04

8 B Stadard mal Dtrbuto umercal etre rereet the robablty that a tadard mal radom varable betwee - ad where µ Hawe Learg Sytem 04

9 C Crtcal Value of t Oe Tal df Two Tal Left Tal t 0 t Rght Tal t t Two Tal t 0 t t Hawe Learg Sytem 04

10 G Crtcal Value of c χ χ to the Rght of the Crtcal Value of χ df Hawe Learg Sytem 04