untitled

Size: px

Start display at page:

Download "untitled"

誉籍
7 years ago
Views:

1 理 (Managerial Statistics) 立理數率理 3/4/000

2 - 料量流理 3 - 索理 4 3/4/000

3 -3 (Model) (Method) 理 (Story) 料 (Data) (Contribution) 論 (SMMDC) 理 5-3 類數量 AHP Fuzzy / 量數量論類料料料理 6 3/4/000 3

4 A.(Descriptive Statistics) 說料 B.(Basic Statistics) 率數率 C. 論 (Inferential Statistics) 量論參數 D.(Applied Statistics): 異數列理量理 7 Required: Excel - 益 - 料行 Option: ( ). SAS: 年. SPSS: 3. MINITAB: 4. Statistica: Statsoft, Inc. (004), Data Analysis Software System, version 理 8 3/4/000 4

5 A. (Descriptive Statistics) 理葉 (Stem & Leaf) 理 0 3/4/000 5

6 Histogram (Spreadsheet 0v*47c) Var = 47 *.779*normal(x, 86.73, 5.874) No of obs K=9 (Histogram) Var K= Histogram (Spreadsheet 0v*47c) Var = 47*.38*normal(x, 86.73, 5.874) 4 K=6 Histogram (006statgrade 0v*47c) Var = 47*4.0769*normal(x, 86.73, ) 7 0 No of obs No of obs 理 Var Var No. of obs K=6 Histogram: Var K-S d=.086, p>.0; Lilliefors p>.0 Expected Normal X <= Category Boundary D-statistics N=47 Mean=86.73 Std=5.87 Max=97.0 min=7.56 Range=4.46 Q-range=7.3 Percentile(%) ( ) 5 ( ) 50 ( ) 75 ( ) 88 ( ) 理 3/4/000 6

7 B. (Basic Statistics) 理 3 (Population): / (Sampling): 料不易 (Sample): ;; 精不參數 (Parameter): ( µ) 量 (Statistic): 數 x x 例料例理 4 3/4/000 7

8 率(Sampling Method) VS 不例理 5 論參數 µ σ 論數率量 x pˆ 理 6 3/4/000 8

9 . 率 (Probability): 量不. 數 (Random Variable): 數數 3. 率 (Probability Distribution): 數率 4.(Sampling Distribution): 量率理 7 (µ, σ, p) 度 (Accuracy): 精度 (Precision): 異數 X X X X X X X X X X 理 8 3/4/000 9

10 兩 (Two Stage Optimization) Output voltage Transistor gain Figure 3. Effect of Transistor Gain on the Output Voltage 理 9 異力力 D C B A B C D 度 (µ, σ, p) 力,, 979,4 7 不良率 (p) 零 0.3% 理 0 3/4/000 0

11 [ 論例 ] 95%,? : ( E) = Z * s( pˆ) n= Z pˆ( pˆ)/ E α / α / [ ]: (Z ) pˆ = 0.5; α = 0.05 n =.96 *0.5*0.5 / 0.03 = 理. 率 (Probability) 率量不兩率例 S={,,3,4,5,6} P()=/6=P()= P( 數 )=P{,3,5}=/ 理 3/4/000

12 率理論 ( ) 率 : 數數 ( ) 率 : 數率 : 率理 : () 率零 () 率零 (3) 聯率率理 3 率類 A B 聯率 : P(AUB)=P(A)+P(B)-P(AB) 率 : P(A B)=P(AB)/P(B) : P(AB)=0 立 : P(AB)=P(A)P(B) 理 4 3/4/000

13 率率立聯率 H (H,) (/) (H,) (/) (H,3) (/) (H,4) (/) (H,5) (/) (H,6) (/) / T (T,) (/) (T,) (/) (T,3) (/) (T,4) (/) (T,5) (/) (T,6) (/) / /6 /6 /6 /6 /6 /6 P({H,3})=/=P({H})P({3})=/*/6 立, 立 {H} {3} 理 5. 數 (Random Variable) 數數 : y=f(x), y; x : 數數 : (X,Y,Z ) : 數連 : 數 P(w ) =p P(w ) =p w w 連數 ( 數 ) X,Y,Z, 數數 [ 例 ]: Y Y(w )=56 [ 例 ]: X X(w )= 女 = 理 6 3/4/000 3

14 3. 率率率不連率 Σ 理 7 F ( x) = f ( w) w x 連率率率率 F ( x) = x f ( w) dw f(x)=f (x) 累數 (Cumulative Distribution Function): 0 F ( x) 率度數 (Probability Density Function): f ( x) 0 3. 率 - 例兩率 : S={MM,MF,FM,FF} 率 : P(MM)=/4; P(MF)=/4; P(FM)=/4; P(FF)=/4. 數 : Y 數 Y(MM)=; Y(MF)=; Y(FM)=; Y(FF)= 理 8 3/4/000 4

15 3. 率 - 率 : y 0 f(y)=p[y=y] /4 / /4 率度數 F(y)=P[Y<=y] /4 3/4 4/4 累數率 f(x) 0.5 <P.D.F.> 0.5 F(x).00 <C.D.F.> x 理 9 x 數數 (Function of Random Variable) x - 0 f(x)=p[x=x] /4 / /4 Y=X+ y 0 f(y)=p[y=y] /4 / /4 Z=X z 0 f(z)=p[z=z] / / 理 30 3/4/000 5

16 (Binomial) X: 數 n: 數 p: 率 X ~ Binomial(n,p) n x n x n P[ X = x] = p q, x = 0,,..., n = x x! ( x n! n x )! [ 例 ]: n=, p=0.5 0 P[ X = ] = = 0.5 P[ X = ] = P[ X = 0] = = * 0.5 = 0.5 = 理 3 0 (Hypo-geometry)- N-S N n-x n x S 理 3 3/4/000 6

17 (Hypo-geometry)- N: 數 S: 數數 n: 數 X: S N S N P [ X = x] = /, x = 0,,...,min( S, n) x n x n [ 例 ]: 30( 5 女 ), 率? P[ X = 3] = / = 3000 /(9* 8* 7*6) 理 33 (Poisson) X: 數率 ; l: 率 x λ P[ X = x] = λ e / x!, x = 0,,... [ 例 ]: 行 5 來 3., 率? P[ X > 7] = x= 8 3. x e 3. / x! = 理 34 3/4/000 7

18 數異數 (Expectation Value): µ = E( X ) = xf ( x) 異數 (Variance): σ ( X µ ) = ( x = E µ ) f ( x) 率 (µ) 異數 (σ ) np npq n(s/n) λ S N S N n n ( )( )( ) N N N λ 理連率 [ 例 ]: 率 : S={,,,...} 率 : P( )=P( )=P( )=/N. 數 : X; X( )=56; X( )=70; X( )=75. 率 : P[a<X<b]=? P[X<x]=? P[X>c]=? 累數 (Cumulative Distribution Function): F(x)=P[X<=65]=0.55 率度數 (Probability Density Function): f(x)=f (x) 理 36 3/4/000 8

19 (Normal Distribution) X ~ N( µ, σ ) f ( x) = exp( ( x µ ) ), < x < πσ Z = ( X µ ) / σ ~ N( 0, ) (Standard Normal Distribution) z f ( z) = exp( ), < z < π z F ( z) = P[ Z z] = f ( y) dy µ 4σ µ σ µ µ+σ µ+4σ z x P[ Z >.645]=0.0 ; P[ Z >.96]=0.05 ; P[ Z >.575]= 理 37 [ 例 ]: 令 X~N(65,00),. P[X<80]=?. P[50<X<70]=? 3. P[ X-65 >0]=? [ ]. P[(X-µ)/σ<(80-65)/0]=P[Z<.5]= = P[(50-65)/0<(X-µ)/σ<(70-65)/0] =P[-.5<Z<0.5]= = P[ X-µ /σ>0/σ]=p[ Z >]=*( )= 理 38 3/4/000 9

20 (Uniform Distribution) X~U(a,b) P.D.F f(x)=/(b-a), a<x<b C.D.F F( z) = P[ X z] = f ( x) dx = ( z a) /( b a), a < z < b z f(x) /(b-a) F(x) F(z) a z b x a b z x 理 39 連數異數 (Expectation Value): 異數 (Variance): µ = E ( X ) = xf ( x) dx σ = E ( X µ ) = ( x µ ) f ( x) dx 率 (µ) 異數 (σ ) µ σ (b-a)/ (b-a) / 理 40 3/4/000 0

21 數異數 E(c)=a; E(a+bX)=a+bE(X); V(c)=0 V(a+bX)=b V(X) E(aX+bY)=aE(X)+bE(Y); V(aX+bY)=a V(X)+b V(Y)+abCov(X,Y) If X and Y are independent, then Cov(X,Y)= 理 4 亂數 (Random Number) ~ U(0,) X~U(0,) Excel: RAND() f(x) F(x) 0 f(x)=, 0<x< x 0 F(x)=x, 0<x< x 理 4 3/4/000

22 亂數 (Random Number) 理論 (i) X ~ F(x) (ii)y=f(x) ~ U(0,) G(y)=P[Y<y] =P[F(X)<y] =P[X<F - (y)] =FF - (y)=y n X~F(x) 亂數 (i) Y~U(0,) n y,,y n (ii) x i =F - (y i ), i=,,n x,,x n F(x) 理 43 [Excel Function for Normal Distribution] p=normdist(x p ); p=normsdist(z p ) x p =NORMINV(p); z p =NORMSINV(p) [ 例 ] Excel 數 n 亂數 x,x,,x n 兩 (i) y =RAND(), y =RAND(),,y n =Rand() (ii) x =NORMSINV(y ), x =NORMSINV(y ),, x n = NORMSINV(y n ) 理 44 3/4/000

23 4. (Sampling Distribution) : 量率 [ 例 ]: X N ( µ, σ ) X n N ( µ, σ / n) X NonNormal 理理 45 X ~ N (0,) : X ~ N (0,); X 4 ~ N (0,/ 4); X 4 ~ N (0,/ 9) X n 理 46 3/4/000 3

24 理 47 見 : 異數, 數 Z= n(x µ )/ σ n t- : 異數, 數 t = n(xn µ )/S : 異數 F- : 兩異數 χ =( n ) S / F = S / S σ : Z=(X-µ)/σ : C =(N-n)/(N-) 理 48 3/4/000 4

25 C. 論 (Inferential Statistics) (Estimation) (Hypothesis Testing) 理 49 (Estimation) (Point estimation): [ 例 ]:,, : x= ; x= ; x3= ; x4= ; x5= ; µ = σ = X σ = σ i ( X / N i µ ) / N 異數 X = S S = = S X ( X i / n i X) /( n ) 理 50 3/4/000 5

26 . (). 參數. 量 3.,(-α) 4. 率臨 5. 臨參數 P[ a' 量 P[ a 參數 b'] = α b] = α 理 5 [ 例 ]. 量 X. X n 3., 4. 臨 5. P[ Z Z = n ( X α / P[ X n n, Z Z n α / Z 參數 α / µ ) / σ Z α / σ / Z µ. N ( µ, σ / n) = α /, Z N (0,) 0.05 ] = α = n µ X =.96 n + Z α / σ / n ] Z α / α Z α / 理 5 3/4/000 6

27 [ 例 ]: 異數令 σ= % [ ]: (Z ) σ = 60; n = 36; x = 000; α = 0.05; Z P[ x Z α / σ / n < µ < x Z P[000.96* 60 / 6 < µ < *60 / 6] = 0.95 P[980.4 < µ < 09.6] = 0.95 α / 0.05 σ ] = α = 理 53 Z α / α Z α / µ µ 不 µ 若 n ( α)n µ 理 54 3/4/000 7

28 [ 例 ]: 異數令 % n = 5; x = 000; s = 50; α = 0.05; t [ ]: (t ) 0.05 P[ t P[ X =.064 α / n t T t α / s/ α / ] = α = n µ X + t α / s/ P[ *50/ 5 µ *50/ 5] = p[ µ 00.64] = 0.95 n 理 55 n] α / t α / α α / t α / [ 例 3]: 異數了 5 x =000 s=00 異數 95% P[(n-)S /χ α/ <σ <(n-) S /χ -α/ ]=- α [ 3]: () n = 5; x = 000; s = 00; α = 0.05; χ 0.975,4 =.40; χ 0.05,4 = P[(5-)00 / <σ <(5-) 00 /.40]=0.95 P[6097<σ <9353]= 理 56 3/4/000 8

29 χ P[χ -α/ < (n-)s /σ < χ α/ ] =- α P[(n-)S /χ α/ < σ < (n-) S /χ -α/ ]=- α 理 57 [ 例 4]:,00 60 率 99% pˆ = X / n; s( pˆ ) = P[ pˆ Z α / * pˆ( pˆ ) / n s( pˆ ) P pˆ + Z α / * s( pˆ )] = α. [ 4]: (Z ) n = 00; pˆ = 60 / 00 = 0.8; S( pˆ ) = α = 0.0; Z = * 0. / 00 P[0.8.58* P ] = 0.99 p[0.77 P 0.873] = 0.99 = 0.088; 理 58 3/4/000 9

30 [ 例 5]: 95%,?.: ( E) = Z * σ / n n = Z σ / E α / α /.: ( E) = Z * s( pˆ) n= Z pˆ( pˆ)/ E α / α / [ 5]: (Z ) pˆ = 0.5; α = 0.05 n =.96 *0.5*0.5 / 0.03 = 理 59 (Hypothesis Testing) 類.(Simple Hypothesis):.(Composite Hypothesis):.(Null Hypothesis H 0 ). 立 (Alternative Hypothesis H ) [ 例 ]: H 0 : µ=60 vs H : µ>60 [ 例 ]: H 0 : µ=60 vs H : µ<60 [ 例 3]: H 0 : µ=60 vs H : µ 理 60 3/4/000 30

31 參 () H 0 H 0 H 0 II (β) α = β = P[Re ject P[ Accept H H 0 ] ] H 0 I (α). α,β. α+β=??? 3. n, α,β 4. Dist Ho-H, β, Power of Test=- β 理 6 [ 例 4]: H 0 : µ=70 vs H : µ=80 σ=65, n=400. α = β = P[Re ject P[ Accept H H 0 ] ] Accept Rejection 理 6 3/4/000 3

32 精神數理 :. 例理立. 例理不立理 : 若 p q iff 若 -q -p : (Negation) : 立 H H 0 料 H 0 H H 0 α 理 63 [ 例 ]σ=30 36, X =750 α=0.05 數 µ=740 了? [ ]: H H 0 : µ = 740 : µ > 740 量 Z = n( X n µ )/ σ ~ N(0,) 論 : a=0.05, 料, 數了. α = 0.05 Accept z x Rejection n 4. c 4. a z = ( x n µ ) /( σ / n) = 4. b 36( ) / 30 = >.645 ( c µ ) /( σ / n) =.645 c = *.645 = < 750 P[ X n > 750] = P[ Z > ( )/(30/ 6)] P[ Z > ] = 0.08< 理 64 3/4/000 3

33 例率 β 力 ( β) 若 µ=745: 若 µ=750: β = P[ X n < c H ] = P[ x n < µ = 745] P[ Z < ( ) / 5] = P[ Z < 0.645] = β = P [ X n < c H] = P[ x n < µ = 750] P[ Z < ( ) / 5] = P[ Z < 0.355] = (µ,β) µ β power 理 65.H 0 H ; a. H H 0 ( H 0 ) b. 立立不不 ( vs ). 量 (Test Statistic) a. 參數 (Point Estimation); b. 量理 66 3/4/000 33

34 3. a. H 0 b. H (Rejection Region) 4. 量落 a. 量臨 (Critical Value); b. 臨數 ; c. p-value 若 p-value<αh 0 5. 論 a. H 0 α b.h 0 α c. H 0 β d.= 理 67 陸理 µ σ Z (a) σ t (b) σ χ (c) P Z (d) 兩 ( 立 ) σ = σ F (e) µ =µ σ σ Z σ σ t σ =σ ( S p ) t (f) σ =σ ( 度 ) t (g) P =P () Z (h) 兩 () 來理理 68 (i) 3/4/000 34

35 [ 例 ]: (t : 兩數, 異數 ) 不力, 樂量異, 料 : Comparing soft-drink bottle fills based on two different pressure settings 5 PSI 30 PSI PSI 30 PSI 數異數數數 0 0 Pooled 異數數 0 度 8 t P ( T = t ) 臨 : = t 0.05 (8) P ( T = t ) 臨 :.0094 = t 0.05 (8) 理 Reject t 0.05 H µ µ 0; H µ µ 0 T = S p 0 : = = 9 ( X X ) ( µ µ ). 540 ( n ) S + ( n ) = ( n ) + ( n ) ( ) + 9 ( ) H p : if t ( 8) =.0 S 9 n n = : t + + α n n or t t n n α 4. H 0 is rejected at α = 0.05 *Because p value = α, we have sufficient evidence that H 0 is not true. So H 0 is rejected 理 70 = S t ( n + n ). 540 Two-tailed Test 3/4/000 35

36 理 7 3/4/000 36

untitled

untitled 領參讀什不論不若不什什不來參不什來立來度讀老度不兩落度行刺讀例讀行力讀兩輪度不浪讀率若度輪行行類不類不論例論留理 1 論論論論論論論論論論論了省省度不例理例念理論度類行聯理論度精利 2 省例行類立省精省益省省利