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Sampling distribution, Point estimates, Interval estimation, Hypothesis testing, Analysis of Variance
Typology: Study notes
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Type I^ error^.^ Power ① (^) Oneftu.^ -^ sided^ tests^ for normal^ mean ② t -^ test (^) with (^) unknown 6 ' and n ⑤ (^) Test (^) for normal variances ④ Test^ for (^) comparison of^ (^2) normal means with known^ variances ⑤ or unknown^ , (^) equal variances Test (^) for correlation (^) coefficients
9 Hypothesis Testing O (^) 9. tp-va P- value (^) is the probability of^ the event that the^ test (^) statistic takes the^ observed
Small ' p
large '
i (^) : (^) Test (^) statistic T = TITI n = t M¥1:^ calculate^ p -^ value Pu. (^ Text^ )^ = pl 121 >
under no^ ,^ =÷E÷^ n Reject Ho it t^ >^ Want for (^) any 6276.2^ , power of^
PC
'
. x'a.m ) > a as^ - I probability of^ Type I^ error^ I^ -^ PCG
I - E. n - I or^ -17 (^) Ago (^) , n - I ⑧ o 9.lt#amanmUpaHdbW~~yi~N( (^) Me
independent Ho :^ Nx -^ - he let Zi^ -^ -^ Xi^ - Yo (^) , Zi -^ N ( (^) Nx- Me ,^6 ×^465 ) IEEE T=¥=5h% Reject Ho (^) Nx- up when^ I-471% (^) ,^ n^ -^ I^ if th^ :^ Mx#^ My t >^ tan-^ I^ it Hit Ux>^ My
(^0) Power function
μ= Nx-^ My^70 play
=pn( This^ >^ tan (^) ,^ - I )
°
Ash (^) increases → g- increases →^ power increases 0 9. Gmparmgtnonorma1mean€ of^ different (^) sample sizes { Xi (^) ,^.^ -^.. Xn^ ) f Yi^ ,^.^.^ - , Yml^ mtn
sie (^) # (^) E. Hi -^ H^ ' Sy
. - this Hi-FI^ ' F (^) , -7 (^) , Sj , Sy ' are (^) independent
E. nwcuy^ ,^ I^ cm-"f -^ him^ -^ I F- (^) Tn N tax- my (^) , #t (^) ) If (^6) ×2= l-cnx-ny,yj TZ
= x }T-(nI
Ymt Yn^ CH) sit (^) cm- HST ① With known^65 by '
Under (^) Ho (^) , Mx- Ny - T
H=lplJT increases as (^) Ifl increases 09.14 (^) -estsfrtheratiooftnenormalvaria## ( Xi^.^.^ -^ -^ -^ Xml^ f^ Yi^ ,^.^ -^ - ,^ Yml^ from^ thnx.^6 ×^4 N^ (Ny (^) , 65 ) Independent Ho (^) : (^) f÷=k Hi : %÷tk We (^) have cn% n (^) x'ni , ' n x'mi ( n-115×^2 -6× 2 :-(htt^ Y6× 5 ×^2 i÷÷÷÷÷÷÷→ Reject Ho (^) if t -^ Fi- E. n - i. (^) my or^ t >^ FE ,^ n^
( (^) FI-E.n-i.mx (^) S¥ , FE.n-i.mu (^) ×S¥ (^) )
FI- d (^) Nish = Fa , vav, E. (^) g.
PC Fs^ .sc^ fI , = #=^ o (^) - N (^) ) =
