Cheat Sheet: Confidence Intervals - Principles of Statistics I | STAT 211, Study notes of Statistics

Download Cheat Sheet: Confidence Intervals - Principles of Statistics I | STAT 211 and more Study notes Statistics in PDF only on Docsity! Stat381 Cheat sheet: Confidence Intervals                       222111,1 2 2 2 1 2 2 21 2 1221 2 2 21 2 1 21212 2 2 121 21 2 2212 21 2 2121 2 2 2 121 2 2 21 2 1221 2 2 21 2 1 2121 2 2 2 1 21 2 2 21 2 22 2 2 1 2 1 222 21 2 2 2 , unequal)&unknown ,( 11 11equal) &unknown ( known) ,( )ˆ1(ˆˆ~ )1( ˆ n)(proportio )1( , )1( )1( )unknown ( )known ( 21 21                         fLfLFSS nSnStXXT nSnS XX nnStXXT nnS XX ,σσ nnzXXZ nn XX nppzpZ npp pp p Sn L Sn LSn nStXT nS X nzXZ n X nn pnn p n n                            Parameters being estimated Begin Derivation with Distribution (D.F.) 100(1-α)% conf. interval                   11 2 2 2 2 2 1 2 1 2 12 2 2 21 2 1 n nS n nS nSnS 2 )1()1( 21 2 22 2 112    nn SnSn S p 1© 2008 Xijin Ge, All rights NOT reserved. Accuracy NOT guaranteed! 2][ :Note 2   tTP 2 2 2 1  Reject Ho Accept Ho Accept Ho Reject Ho Accept Ho Reject Ho Reject Ho 211 210 : :     H H 211 210 : :     H H 211 210 : :     H H Left Tailed Right Tailed Two tailed http://www.pindling.org/Math/Statistics/Textbook/Chapter8_two_population_inference/proportion_independent.htm http://library.beau.org/gutenberg/1/0/9/6/10962/10962-h/images/069.png  observedTT P valueP  observedTT P valueP             .0 if P2 ;0 if P2 P valueP observedobserved observedobserved observed TTT TTT TT Hypothesis testing on the difference between two means: equal variances Null hypothesis: Ho: µ₁ - µ₂ =D, (D is often zero). . observedfor valuePor level cesignificangiven aat valuescritical determine to tableT Usefreedom. of degrees 2 with on distributi T a have will then true,is hypothesis null theIf 5. )11( )( :T statistic test theCalculate .4 2 )1()1( variancepooled theEstimate .3 r)denominato in the 1(with , variancessample theCalculate .2 . and Calculate 1. :equal be toassumedbut unknown are ),( variancesIf 21 21 2 11 21 2 22 2 112 2 2 2 2 1 21 2 2 2 1 T nn T nnS DXX T nn SnSn S S nSS XX p p p          Quick recipe #3: T test with equal variances In Excel: TTEST(array1,array2,tails,2) Normality required 5 Hypothesis testing on the difference between two means: unequal variances Null hypothesis: Ho: µ₁ - µ₂ =D, (D is often zero).       . observedfor valueP levelthe cesignificangiven aat value critical determine to tableT Usefreedom. of degrees with on distributi T a have will then true,is hypothesis null theIf 5. )( )( :T statistic test theCalculate 4. 11 : freedom of degrees iteSatterthwa-Smith theCalculate .3 r)denominato in the 1(with , variancessample theCalculate .2 . and Calculate 1. :unequal andunknown are ),( variancesIf 2 2 21 2 1 11 2 2 2 2 2 1 2 1 2 1 2 2 2 21 2 1 2 2 2 1 21 2 2 2 1 T T nSnS DXX T n nS n nS nSnS nSS XX              Quick recipe #4: T test with unequal variances In EXCEL: TTEST(array1,array2,tails,3) Normality required. Safe to use even variances equal. 6 Hypothesis testing on the difference between two means: Paired data Null hypothesis: Ho:   . observedfor valueP or level cesignificangiven aat valuecritical determine to tableT Usefreedom. of degrees 1on with distributi T a have will then true,is hypothesis null theIf 5. :statistic test theCalculate .4 1 and , : variancesand mean sample theCalculate .3 .0 :is hypothesis null The problem. sample -one a into problem sample- twoa converted and , variablerandom new a defined have We.2 : difference thecalculate ,2,1 where),,(n observatio pairedeach For 1. :paired are , samples random twoIf 222 2 2 1221 2 D T nT nS D T n DnDDD S n DDD D SD D YXD DniYX YX D n D n D iii iii              Quick recipe #5: Paired T test 0 YX  In EXCEL: TTEST(array1,array2,tails,1) Normality required 7