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효리 강
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1 5.8 PROC UNIVARIATE (hitogram, tem and leaf plot, box-whiker plot), (p- ). Univariate( ).. NORMAL (Shapiro- Wilk Kolmogorov-Smirno D- OUTPUT( SAS ). PROC MEANS PROC MEANS. (moment) E( X ). k Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 9

2 N= ( ) (weight) xi (mean) x = (um) x i n (td) = (kewne) ( xi x) n n xi x ( ) ( n )( n ) 3 (variance) ( xi x) = n (kurtoi) n( n + ) x ( ( n )( n )( n 3) i x ) 4 3( n ) ( n )( n 3) ( ) (um of quare) x i (adjuted) ( x i x) (CV) CV = 00 (STDERR) x n,. (mode) ( ). ( ~. µ 0 = 00 ). MU0. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 30

3 t ( 4 ) (nonparametric, ditribution-free tet) (ign tet). Shapiro Wilk ( ). AL.. 75% (Q3), 50%, 5% Q( ).. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 3

4 PLOT. Graphic.. +. AL.?.. Q3 Q ( : 9 ) HISTOGRAM.. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 3

5 .. AL... Shapiro-Wilk. Q-Q plot( ). Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 33

6 A:\JUNE\UNIVAR.doc x ± t( n ; α / ) n 5.9 PROC TTEST (, ), t-, µ σ /.. n Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 34

7 5.9. PROC TTEST t-.. σ,σ,..... Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 35

8 : H µ µ 0 (.) 0 : = : ( ) H a : µ µ 0 ( ) H a : µ > µ H a : µ < µ : ( x, x,..., x n ) x, ( x, x,..., x ) x, n = σ σ ) ( σ =,. σ (pooled x variance). x ( µ µ ) = 0 T = ~ t( df = n + n ), p + n n p ( n = ) + ( n ) n + n ( µ µ 00(-α)% : ) (( x x ) t n + n ) *,( x x) t( / ; ) * p + + α n n n + n p + n ( α / ; n ) A, B 8. x = 9, =. 39, x = 93, = ( =0.05).. (adjuted) t-. T = x x ( µ µ ) = 0 ~ t( df p + n n * = ( / n ) n + ( + n n ) ( / n) + n + ) Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 36

9 CLASS.txt.. 90%. : H µ µ 0 ( ) 0 : = : H µ µ 0. a :. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 37

( µ µ ) 90%(Alpha=0. ) 5.9.3 t- t-. EXAMPLE A, B. 8... ( =0.

10 ( µ µ ) 90%(Alpha=0. ) t- t-. EXAMPLE A, B ( =0.05) A B : H : µ µ µ 0 (A, B ) 0 a = b d = : H : µ µ µ 0 (A, B ) 0 a b d d µ d : T = d = = =. 46, / n.67 / 8 d d t( α / ;7) =.365. Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 38

11 A:\JUNE\TTEST.doc.. : : %. A:\JUNE\TTEST.doc A, B 0.. ( : ) A: B: % Sehyug Kwon, Dept. of Statitic, HANNAM Univerity Spring, 004 copy right all right reerved. 39

확률과통계 강의자료-1.hwp

확률과통계 강의자료-1.hwp 1. 통계학이란? 1.1 수학적 모형 실험 또는 증명을 통하여 자연현상을 분석하기 위한 수학적인 모형 1 결정모형 (deterministic model) - 뉴톤의 운동방정식 : - 보일-샤를의 법칙 : 일정량의 기체의 부피( )는 절대 온도()에 정비례하고, 압력( )에 반비례한다. 2 확률모형 (probabilistic model) - 주사위를 던질 때