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1 ( ( ( ( 00 1 (P (P (P (P.15.1 (P (P (P (P (P ( P (P (P (P (P (P (P (P (P (P (P (P (P (P

2 6.1 (P (P (P (P (P (P (, P (, P (P.103, (P (P (P (P (, P (, P t (, P (P ( ( 1,, P (P ( 48 ( α β û i R (

3 (P.1 1. (P.4 1. ( , (a (b (c ( (d ( ( (P (P.3 (P.3 1. ( ( ( ( 1997 GNP GNP (P.8 1. (P P ( (P P (P.5 (0 : 1.3 (P

4 (P.16 ( ( m 1 a 0 a 1 f 1 m a 1 a f m k a k 1 a k f k 3. m 1 a 0 + a 1, m a 1 + a,, 4. m k a k 1 + a k x 1 (f 1m 1 + f m + + f k m k 1 k f i m i ( k f i x m i f (P.15 i x 1 ( ( (.1 (P.15 x 1, x,, x (P.15 x 1 (x 1 + x + + x 1 1. (P.5 x 1 ( x i. (P.18 (s s 1 ((x 1 x + (x x + + (x x 1 (x i x x 1 x i

5 s s 1 x i x s 1 (x i x 1 (x i xx i + x 1 ( k f i m i x + x 1 ( x i x x i + x 1 ( k f i m i x 1 ( x i x + x 1 k f i m i x 1 ( x i x 1 x i x s 1 ( ( ( ( ( (P.5 +( s 1 ( ( ( ( s 1 0 ( s (P.17.1 (P.16 s 1 k f i (m i x x 1 k f i m i s 1 k f i m i x 3 s 1 1 k f i (m i x k f i (m i xm i + x 1 ( k f i m i x k f i m i + x s 1 0 ( k f i s ( 1 50 ( 75 ( (

6 ( (P. f(t 0 t 100 (x 1, y 1, (x, y,, (x, y f(t t 1 (x i x s xy s xy 1 ( (x 1 x(y 1 y + (x x(y y + t 1 (x i x(y i y + + (x x(y y (y i y (x i x(y i y s xt + s xy t + s y 1 x i y i xy D s xy s xs y 0 r s xy s x s y s x 1 (x i x, s y 1 (y i y, s x, s y x y r > 0 (x y 3.1 ( P.7 r < 0 (x y r 0 (x y 1. A r t f(t 1 s xy > 0 (x y s xy < 0 (x y s xs 1, y s xy 0 (x y 1 s xy 1, s x s y (, (x i xt (y i y t ( 1988 r 1 (x y r s xy r 1 (x y r 1, 1 x y (r 1 r 1 3 (P.7. a A a A 1 r 1 a A 3. b A b / A 4

7 4. φ 5. Ω A, B 8. A B φ A B 7. A B A A c B A A B 8. A B A B. A {, 4, 6} 9. A B A B 10. A B A B 6. C {1, 3} 11. A c Ω A A C φ A C 1. ( (A B C A (B C A B B A A (B C (A B (A C (A B c A c B c 3. (P.31 ω 3 {H, T, H}, ω 4 {H, T, T }, 1. ( ω 5 {T, H, H},. ω ω 6 {T, H, T }, (1,, 3, 4, 5, 6 ω 7 {T, T, H}, ω 8 {T, T, T } 3. Ω 3. Ω {ω 1, ω, ω 3, ω 4, ω 5, ω 6, ω 7, ω 8 } 4. E 4. Ω (, 4, 6 E {ω 1, ω, ω 5, ω 6 } 5. φ F {ω, ω 3, ω 5 } Ω {1,, 3, 4, 5, 6} 3. A c {1, 3, 5} 4. B {1,, 3, 4} A B A B {1,, 3, 4, 6} 5. A B A B {, 4} A A c φ A A c 3 1. H T. 8 ω 1 {H, H, H}, ω {H, H, T }, 5. F 5

8 6. E F {ω 1, ω, ω 3, ω 5, ω 6 } E F {ω, ω 5 } 7. E c {ω 3, ω 4, ω 7, ω 8 } F c {ω 1, ω 4, ω 6, ω 7, ω 8 } 8. (E F c {ω 4, ω 7, ω 8 } E c F c {ω 4, ω 7, ω 8 } (E F c E c F c 9. (E F c {ω 1, ω 3, ω 4, ω 6, ω 7, ω 8 } E c F c {ω 1, ω 3, ω 4, ω 6, ω 7, ω 8 } 1. 0 P (A 1 (φ (A (Ω (φ 0 0 (A (Ω 1 (E F c E c F c. P (A c 1 P (A 3.3 (P.3 1. (A A. P (A A P (A (A (Ω Ω {1,, 3, 4, 5, 6} (Ω 6. A {1, 3} (A P (A 6 3. B {, 4, 6} (B 3 P (B C {1} (C 1 P (C 1 6 (Ω (A + (A c (Ω 3. A B P (A P (B (A (B (Ω (P (P.34 P (A B P (A + P (B P (A B (A (A B + (A B, (B (B A + (A B, (A B (A B + (B A + (A B (A B, (B A (A B (A + (B (A B (Ω. A B P (A B 0 P.35 P (A B P (A + P (B 6

9 (P P (A B B P (E M A P (E M P (E M/P (M. (P.36 P (A B P (A BP (B P (A B (A B (B P (A B P (B (A B/(Ω (B/(Ω B A A { } B { } P (A B P (AP (B A B { } P (A B (P.36 P (E 300 (J (M (M c 4.1 (P.43 (E (J (M 30 0 (M c % X 0 X 1 (a X({ } 0, X({ } 1 P (E M P (E M P (M EP (E P (E 300/( , P (M E 0.3 P (E M P (M EP (E (b P (E M 0.18 ( ( P (M P (Ω M P (E J M P (E M (J M P (E M + P (J M P (M EP (E+P (M JP (J P (E M 0.18/( /13 5. P (A B P (A A B 6. A B 4 (P (P , 1 X X X X ω X x P (X(ω x P (X x 1, x 0, 1 7

10 X 0, 1 X 0 1 1/ 1/ 1 X x 1, x,, x i, p 1, p,, p i, X x 1 x x i p 1 p p i 1 x i p i X P (X x i p i p i X H H c H c f(x i X 1 p i f(x i 0, i 1,, p i f(x i 1 i i X x F (x F (x P (X x r p i r f(x i, r x r x < x r+1 F ( 0, F ( 1 X! X C x x!( x! X /8 3/8 3/8 1/ (P , H H c P (H 0.3, P (H c 1 P (H X 1 3 X H H H H H H c H H c H p i X H c H H H c H H c p i f(x i, i 1,, H c H c H H c H c H c P (X , P (X , P (X , P (X , X p x P (X x P (X x C x p x (1 p x, x 0, 1,, 8

11 p 0.3, 3 P (X 0 3 C ( P (X 1 3 C ( P (X 3C 0.3 ( P (X 3 3 C ( (P.47 X < x P (X < x F (x P (X < x x F (x P (a < X < b F (b F (a b b F ( 0, F ( 1 a f(tdt f(xdx f(xdx a f(xdx p i f(x i f(x f(x 4. (P.49 X (a, b f(x 0, f(xdx 1 b X P (X x P (x X x P (a X b P (a < X b P (a X < b P (a < X < b x x f(tdt 0 X g(x P (a < X < b f(xdx a g(x E ( g(x ( a < b g(x i p i g(x i f(x i, i i p i f(x i 0, i 1,, p i E ( g(x f(x i 1 g(xf(xdx, i i 1. X E(X X, g(x X x i f(x i, i E(X xf(xdx, µ, ( µ x. X V(X (, g(x ( 9

12 . 4. (P.51 V(X E(X µ V(X E ( ( (x i µ f(x i, i (x µ f(xdx, σ, ( σx V(X E ( ( E(X µx + µ E(X µe(x + µ E(X µ µ E(X X V(X X ( ( V(X 3. a, b 4.3 (P.5 V(aX + b a V(X E(aX + b aµ + b 1. a, b 4.1 (P.51 E(aX + b ae(x + b X ( ((ax V(aX + b E + b E(aX + b E ((ax aµ E ( a ( a E ( ( a V(X E(aX + b i (ax i + bf(x i a x i f(x i + b f(x i i i ae(x + b f(x i 1 i X E(aX + b a + b (ax + bf(xdx xf(xdx f(xdx ae(x + b f(xdx 1 X x 1 x x 3 x 4 x 5 x p 1 p p 3 p 4 p 5 p E(X 6 x i p i

13 E(X 6 x i p i V(X E(X µ 91 ( σ V(X. X ( Z σ (P.5 E(Z 0, V(Z (P.51, 4.3 (P.5 a 1 σ, b µ σ E(Z E( σ 1 E( σ 1 ( E( σ 0 V(Z V( σ 1 σ V(X 1 : (p + q x0 C x p x q x E(X p, V(X p(1 p E(X x x x x xf(x x C x p x (1 p x! x x!( x! px (1 p x! (x 1!( x! px (1 p x p ( 1! (x 1!( x! px 1 (1 p x x p! (1 x!( x! px p x x p x C x px (1 p x p 1, x x 1 V(X E(X µ E(X X X(X 1 + X E(X E ( X(X 1 + E(X V(X E ( X(X 1 + µ µ 1 x E ( X(X 1 x(x 1f(x x x(x 1 C x p x (1 p x f(x C x p x (1 p x! x!( x! px (1 p x, x 0, 1,,,, C x p x (1 p x 1 x x x! x(x 1 x!( x! px (1 p x! (x!( x! px (1 p x ( 1p x (! (x!( x! px (1 p x 11

14 ( 1p! (1 x!( x! px p x x ( 1p x C x px (1 p x X \ Y y 1 y y m (X ( 1p, x x V(X E(X µ E ( X(X 1 + µ µ ( 1p + p p p + p p(1 p X Y X i, Y j (i, j 1,, 3, 4, 5, 6 P (X i, Y j P (X ip (Y j 1. p j, j 1,,, m 36 X Y y j X Y Y A, B (P.38: P (A B P (AP (B x 1 p 11 p 1 p 1m p 1 x p 1 p p m p x p 1 p p m p p 1 p p m 1 (Y 1. p i, i 1,,, X, Y 3. 1 Y X x i X 4.3 (P.54 m p i p ij f(x i P (X x i X, Y j1 f(x i X p j p ij f(y j P (Y y j f(y j Y P (X x i, Y y j p ij f(x i, y j i 1,,,, j 1,,, m f(x i, y j X \ Y y 1 y y m x 1 p 11 p 1 p 1m x p 1 p p m..... x p 1 p p m j1 m p ij m p i p j 1 j1 (P.55 A, B (P.36: P (A B P (A B P (B 1

15 Y y j X x i P (X x i Y y j P (X x i, Y y j P (Y y j Y y j X f(x i y j f(x i y j f(x i, y j f(y j A, B (P.38: P (A B P (AP (B X x i Y y j Y Y g(x, Y Y E(Y y j p ij y j f(x i, y j i j i j y j p ij y j p j y j f(y j j i j j µ y X ( x g(x, Y ( x V(X E ( ( x (x i µ x p ij i j (x i µ x f(x i, y j i j i (x i µ x j p ij i (x i µ x p i P (X x i, Y y j P (X x i P (Y y j i σ x (x i µ x f(x i f(x i, y j f(x i f(y j p ij p i p j i, j X Y (P.56 g(x, Y E ( g(x, Y E ( g(x, Y i i g(x i, y j p ij j g(x i, y j f(x i, y j j X X g(x, Y X E(X x i p ij x i f(x i, y j i j i j x i p ij x i p i x i f(x i i j i i µ x Y (Y µ y g(x, Y (Y µ y V(Y E ( (Y µ y (y j µ y p ij i j (y j µ y f(x i, y j i j j j σ y (y j µ y i (y j µ y f(y j p ij j (y j µ y p j X Y (X µ x (Y µ y g(x, Y ( x (Y µ y Cov(X, Y E ( ( x (Y µ y (x i µ x (y j µ y p ij i j (x i µ x (y j µ y f(x i, y j i j 13

16 1. X, Y 4.5 (P.57 E(X ± Y E(X ± E(Y E(X ± Y (x i ± y j p ij i j x i p ij ± y j p ij i j i j E(X ± E(Y. X Y 4.6 (P.57 E(XY E(XE(Y E(XY x i y j p ij i j x i y j p i p j i j x i p i y j p j i j E(XE(Y p ij p i p j 3. X, Y 4.7 (P.58 Cov(X, Y E(XY E(XE(Y Cov(X, Y (x i µ x (y j µ y p ij i j (x i y j µ x y j µ y x i + µ x µ y p ij i j x i y j p ij i j µ x y j p ij i µ y x i p ij i + µ x µ y i i j j j p ij x i y j p ij µ x µ y µ y µ x + µ x µ y j x i y j p ij µ x µ y i j E(XY E(XE(Y Cov(X, Y E ( ( x (Y µ y E ( XY µ x Y µ y X + µ x µ y E(XY E(µ x Y E(µ y X + µ x µ y E(XY µ x E(Y µ y E(X + µ x µ y E(XY µ x µ y µ y µ x + µ x µ y E(XY µ x µ y E(XY E(XE(Y 4. X Y 4.6 E(XY E(XE(Y Cov(X, Y 0 5. ρ xy (P.58 ρ xy Cov(X, Y V(X V(Y Cov(X, Y σ x σ y 6. X Y Cov(X, Y 0 ρ xy 0 7. X, Y V(X ± Y V(X ± Cov(X, Y + V(Y 14

17 X Y 8. 1 ρ xy 1 V(X ± Y ( ((X E ± Y E(X ± Y ( ((X E µx ± (Y µ y E ( ( x ± ( x (Y µ y +(Y µ y E ( ( x ± E ( ( x (Y µ y + E ( (Y µ y V(X ± Cov(X, Y + V(Y t f(t V(xt y t f(t 0 t E(X E( i V(xt y V(xt Cov(xt, y + V(y t V(x tcov(x, y + V(y D ( Cov(x, y V(xV(y 0 ( Cov(x, y V(xV(y 1 1 Cov(x, y V(x V(y 1 1 ρ xy 1 ρ xy 1 i ρ xy 1 9. X Y i 4.8 (P.59 V(X + Y V(X + V(Y V(X + Y V(X + Cov(X, Y + V(Y Cov(X, Y 0 V(X + Y V(X + V(Y 10. X 1, X,, X µ σ i 1,,, E(X i µ, V(X i σ X 1 X i 4.9 (P.59 E(X µ, V(X σ i i i µ V(X V( i i σ X i E( X i 1 E(X i 1 µ X i V( X i 1 V(X i 1 σ 4.5 (P (P (P (P.5 15

18 4.1 (P.59 X, Y X \ Y c P (X, Y 0 P (X Y 0 P (Y c c c 0.4. X Y X \ Y 0 1 X 1 c Y X E(X i x i p ij j x i p i i V(X E ( ( x E(X µ x x i p ij µ x i j 5. Z X + Y Z P (Z 1 P (X 1, Y P (Z P (X 1, Y 1 + P (X, Y P (Z 3 P (X, Y Z Z 1 3 P (Z Y E(Y i y j p ij j y j p j j x i p i µ x i Y 0 X P (X 1, Y 0 P (X 1 Y 0 P (Y V(Y E ( (Y µ y E(Y µ y yj p ij µ y i j j y j p j µ y

19 7. X Y Cov(X, Y E ( ( x (Y µ y E(XY µ x µ y x i y j p ij µ x µ y i j X Y ρ xy Cov(X, Y V(X V(Y (P.65 (χ t 1. x µ. ( ( µ 3. 1 f(xdx 1 N(0, 1 X N(µ, σ ( Z N(0, 1 (P σ X 1, X,, X X i µ σ X 1 X i N(µ, σ (P ( σ/ N(0, 1 5. (P.67 F (x F (x P (X x x f(tdt 5.1 (P.65 f(x ( 1 f(x exp 1 (x µ πσ σ exp(x e x π (, e.7188 ( E(X µ, V(X σ µ σ N(µ, σ X N(µ, σ X N(µ, σ 5.1 f(t (P.68, P.45 (P.68, P.45 N(0, 1 Z N(0, 1 P (Z > 1.96 N(0, 1 Z z P (Z > z P (Z > z α z 100α % P ( Z > z α P ( Z > z α z 100α/ % P (Z >

20 5.1 (P.68 P (Z 1.64 P (Z > (P.69 P (Z < P (Z (P.69 P (Z < 1.96 P (Z > (P.69 P ( 1.96 < Z < P (Z > 1.64 P (Z > (P.70 P (0.5 < Z < 1.96 P (Z > 0.5 P (Z > (P.71 X N(5, P (6 < X < (P.7 Z N(0, 1 1. P (Z P (Z < P (Z > P ( 0.37 < Z P (Z > 0.37 P (Z > P (0.55 < Z < 1.67 P (Z > 0.55 P (Z > Z N(0, 1 σ Z X 5 N(0, 1 P (6 < X < 8 P ( 6 5 < X 5 P (0.5 < Z < 1.5 < 8 5 P (Z > 0.5 P (Z > i.e., X N(, 3, i.e., Z X N(0, (P P (X % P ( X P (Z < 1. X X N(60, 15 Z X Z N(0, 1 P (Z > z z 1.96 P (Z > P ( X 60 > P (X > P (.08 < Z < 0.1 P (0.1 < Z <.08 P (Z > 0.1 P (Z > (P.7 X N(, 9,. P (X < 10 P ( X < P (Z < P (1 < X 4.7 P ( 1 < X P ( 0.33 < Z <

21 4. P (3. < X < 7.7 P ( 3. < X 3 3 P (0.4 < Z < 1.9 < P ( 1.3 < X < 1.19 P ( 1.3 < X < P ( 1.1 < Z < (P.75 1 (P.95 T T f(x 1, X,, X X S 6.1 (P.77 (X 1, X,, X X 1, X,, X i 1,,, (1 4.9 (P.59 X (X 1, X,, X (x 1, x,, x X X 1, X,, X X N(µ, σ X µ X 1 (P.66 P X i (3 E(X µ V(X σ S X ( ( 4.4 P.5 S 1 1 (X i X E(X i µ, V(X i σ X X 1 X i E(X µ, V(X σ ( i X i N(µ, σ σ Z X E(X σ/ V(X/ 19

22 1: N(0, 1 P.68, 45 Z 1 α Prob(Z > z α exp( 1 z α π x dx z α α z α

23 ( P (450 X 500 X P (450 X 500 Z N(0, (P.81 E(Z 0 V(Z 1 Z (4 Z σ S (3 6.1 (P.81 A Z S/, S 1 1 (X i X σ 50 ( 100 X X 1 X i Z N(0, (P.81 P ( 450 µ σ/ σ/ 500 µ σ/ P ( 30/ Z 64 30/ 64 P ( 0.75 Z P (Z > 0.75 P (Z > µ 550 (1, ( P (X > 600 P ( σ/ > 600 µ σ/ (3, ( (1, (3, (4 X i ( P (Z > 50/ 100 P (Z > 0.08 (, (3, (4 X (4 σ S % Z σ/ Z N(0, P (X > (P (P i X i N(µ, σ i 1,,, X i N(µ, σ σ/ N(0, 1 X 1, X,, X µ 30, σ 30, 64 1

24 : χ χ (k P.46 «k 1 k x 1 exp( 1 xdx Z α Prob(U > χ 1 α χ Γ( k α α k

25 1. 6. (P.83 U ( X i µ χ ( σ χ (. 6.3 (P.83 µ X U χ (5 P (U > (P (P (P ( 1S σ χ ( 1 P (S < σ ( ( 1S P (S < σ P σ < ( 1 P (U < U χ (16 P (U < 3 1 P (U > (P.86 Z N(0, 1, U χ (k, Z U 3: t t(m P.47 Z m+1 Γ( α P (T > t α 1 t α Γ( m mπ 1 (1 + x m m+1 α m U ( X i X ( 1S σ σ χ ( S (X i X ( ( 6.1, P , 0.990, 0.975, 0.950, 0.050, 0.05, , dx 3

26 T Z U/k t(k k t t(k t ( 6.3, P , 0.05, 0.05, 0.010, ( 6.3 k t(k N(0, 1 3 (P.47 m 1 (P.45 T t(10 P ( T > (P (P.87 i 1,,, X i N(µ, σ X 1, X,, X 6.3 (P.83 U ( 1S σ χ ( 1 Z U ( T Z U/( 1 t( 1 σ/ ( 1S / σ 1 σ/ S σ S/ (P.86 T S/ t( 1 1 t X 1 X i, S 1 1 (X i X T S/ σ/ S/ t( 1 N(0, 1 (5.4 (P.66 t( (P.86 i 1,,, X i N(µ, σ X 1, X,, X X 1, X,, X ( X N(µ, σ 7 (P.93 µ σ ( Z σ/ N(0, 1 1. ( 4

27 . (a θ(x 1, X,, X X 1, X,, X. 1 E(X i x 1, x,, x 1 µ 7.1 (P.94 µ 1. X 1, X,, X. µ (a X 1 X i µ (b S 1 (X i X σ 1 (X i X 3. ( (Xi µ ( (a x 1 x i µ (X i µ (X i µ( (b s 1 (x i x σ 1 + ( 7. (P (P.95 θ θ θ ( θ θ(x 1, X,, X E( θ θ θ θ E(S θ 1 E( E( θ θ 1 θ(x 1, x,, x (b X µ E(X E( 1 X i E(X µ X µ (c S σ 4. µ σ (X i µ ( (X i µ + ( (X i µ ( +( (X i µ ( (X i µ ( (X i X 5

28 1 ( 1 E (X i X 1 ( 1 E (X i µ ( 1 ( E(X i µ E( ( σ σ 1 1 (σ σ σ E(X i µ σ, E( σ / ( 4.9 P.59 E(S σ S σ. (P.96 θ θ θ ( θ (1, θ (,, θ (, θ ( θ θ θ plim θ θ (a θ θ µ E( θ θ lim V( θ 0 (b µ X 3. (P.98 θ θ 1 θ V( θ 1 < V( θ θ 1 θ θ θ ( θ θ θ ( (a 3 X 1, X, X 3 µ σ i 1,, 3 X i N(µ, σ µ X 1 X i E(X µ V(X σ V(X V( 1 3 X X X 3 V( 1 V(X σ 0 3 X 1 + V( 1 3 X + V( 1 3 X V(X V(X V(X 3 X µ 1 9 σ σ σ 1 3 X X X 3 X 1 4 X X X 3 E(X 1 3 E(X E(X E(X µ µ µ E( X 1 4 E(X E(X E(X µ + 4 µ µ µ X, X µ 6

29 σ 3 V( X V( 1 4 X X X 3 V( 1 4 X 1 + V( 4 X + V( 1 4 X V(X V(X V(X σ σ σ (, P.99 σ σ X 1, X,, X i 1,,, X i N(µ, σ 6 16 σ V(X < V( X X X Z (b X 1, X, σ/ N(0, 1, X µ σ X 1 X i P ( Z < z α/ 1 α α 0.05 µ X P ( Z < z α/ α (P µ (a X N(µ, σ (P.45 α z α/ P ( Z < z α/ P ( Z < z α/ 1 α P ( σ/ < z α/ 1 α P (X z α/ σ < µ < X + z α/ σ 1 α σ σ µ (X z α/, X + z α/ 1 α (b ( σ σ (X z α/, X + z α/ ( 1 α µ σ X z α/ σ X + z α/. σ ( *** *** X x x 1 x i 3. 7

30 σ σ (x z α/, x + z α/ 1 α µ σ x z α/ x + z α/ σ 7.3. (, P.101 σ σ t X 1, X,, X 7.1 (P.101 N(µ, 16 i 1,,, X i N(µ, σ x µ Z N(0, 1 α 0.05 P ( Z > z α/ 1 α z α/ σ σ 1 α µ (x z α/, x+z α/ ( , µ (., 4.18 t α/ ( (P.108 i 1,,, X i N(µ, 3 5 x , 0.95 µ Z N(0, 1 α 0.05 P ( Z > z α/ 1 α z α/ 1.96 α 0.10 z α/ σ σ 1 α µ (x z α/, x+z α/ 0.95 µ ( , (7.13, µ ( , (7.04, Z σ/ N(0, 1 σ S T S/ t( 1 ( 6.5 P.86 t (P.47 α P ( T < t α/ ( 1 1 α 11, α 0.05 P ( T < t α/ (10.8 P ( T < t α/ ( 1 1 α P ( S/ < t α/( 1 1 α P ( X t α/ ( 1 S < µ < X +t α/ ( 1 S 1 α µ (X t α/ ( 1 S, X + t α/ ( 1 S 1 α (X t α/ ( 1 S, X + t α/ ( 1 S ( 1 α µ ( X t α/ ( 1 S 8

31 X + t α/ ( 1 S X, S x, s x 1 (8.634, x i, s 1 1 (x i x (x t α/ ( 1 s, x + t α/ ( 1 s 7.4 (P.108 GNP 1 α µ x t α/ ( 1 s 0.9, 0.95 x + t α/ ( 1 s 0.90 µ ( , µ ( , (8.13, x, s 7. (P.10 N(µ, σ 9 x 1 x i x 3., s µ 1 ( , α 0.05 ( P S/ < t α/( 1 1 α t α/ ( α µ (x t α/ ( 1 s, x + t α/ ( 1 s ( , µ (1.586, (P.108 N(µ, σ 1 s 1.03 x 10.5, 13 s , 0.95 µ α 0.10 t α/ ( ( P S/ < t α/( 1 1 α α 0.10 t α/ ( α 0.05 t α/ ( α µ (x t α/ ( 1 s, x + t α/ ( 1 s 4. s 1 1 (x i x 1 ( x i x 1 1 ( ( α 0.05 t α/ ( α µ (x t α/ ( 1 s, x + t α/ ( 1 s 0.90 µ ( , (3.690,

32 0.95 µ ( , (3.576, 4.84 P (X z α/ σ < µ < X + z α/ σ 1 α X x 1 α µ µ ( : ( 6.1, P.81 σ σ P (x z α/ < µ < x + z α/ 1 α ( X 1, X,, X i E(X i µ V(X i σ X 1 X i ( 100 σ ( 100 σ S σ/ N(0, 1 X E(X V(X N(0, 1 S/ N(0, 1 ( Z S/ (X i ( X E(X µ, V(X σ 4.9 (P.59 P ( Z < z α/ 1 α P ( S/ < z α/ 1 α σ P (X z α/ S < µ < X + z α/ S 1 α ( 100 σ/ N(0, 1 Z σ/ P ( Z < z α/ 1 α P ( σ/ < z α/ 1 α X, S x, s 1 α µ s s (x z α/, x + z α/ 7.3 (P ,

33 N(µ, σ 5097 x 604, s , 0.95 µ 5097 t ( P ( ( 1S χ P S/ α/ ( 1 < σ < < z α/ 1 α α 0.10 z α/ α 0.05 ( ( 1S z α/ α µ s s (x z α/, x + z α/ 0.90 µ ( , (597.7, µ ( , (596.5, P ( χ 1 α/ ( 1 < U < χ α/ ( 1 1 α P ( χ ( 1S 1 α/ ( 1 < < χ α/ ( 1 1 α σ ( 1S χ 1 α/ ( 1 1 α 4. 1 α σ χ α/ ( 1, ( 1S χ 1 α/ ( 1 5. S s 1 α σ ( ( 1s χ α/ ( 1, ( 1s χ 1 α/ ( 1 s 1 1 (x i x (P.103, s 17. X 1, X,, X 0.95 σ i 1,,, X i N(µ, σ ( 6.3 (P.83 U ( X i X σ S 1 1 ( 1S σ χ ( 1 ( 1s (X i X ( χ α/ ( 1, χ 1 α/ ( σ 1. 1 α/ χ 1 α/ ( 1 χ α/ ( (P (P.104 N(µ, σ 0 0, α 0.05 P ( χ ( 1S 1 α/ ( 1 < σ < χ α/ ( 1 1 α (P.46 ( , χ 1 α/ χ α/ ( α σ ( ( 1s (( (0 117., (9.948, χ 1 α/ ( 1 α/ 1 α/ 7.5 (P.109 N(µ, σ 1 s , 0.95 σ 31

34 1 P ( χ ( 1S 1 α/ ( 1 < σ < χ α/ ( 1 1 α (P.46 α 0.10 χ 1 α/ ( , χ α/ ( α 0.05 χ 1 α/ ( , χ α/ ( α σ ( ( 1s ( 1s χ α/ ( 1, χ 1 α/ ( σ ((1 1.8 (1 1.8, (1.565, σ ((1 1.8 (1 1.8, (1.405, (0.608, σ (( ( , (0.548, (P.105 ( i X i 1 X i 0 R X i R 1 p P (X i 1 p X i E(X i 1 P (X i P (X i 0 p V(X i (1 p P (X i (P (P.108 GNP 0.9, 0.95 x 4., s 1 13 (x i x P ( χ ( 1S 1 α/ ( 1 < σ < χ α/ ( 1 1 α (P.46 α 0.10 χ 1 α/ ( , χ α/ ( α 0.05 χ 1 α/ ( , χ α/ ( α σ ( ( 1s ( 1s χ α/ ( 1, χ 1 α/ ( σ (( ( , (0 p P (X i 0 p(1 p P (4.1 (4.14 p X X R 1 X i ( p X p E(X 1 E(X E(X p V(X 1 V(X V(X p(1 p X X 1, X,, X ( 6.1, P.81 p(1 p E(X p, V(X Z X E(X X p N(0, 1 V(X/ p(1 p/ 3

35 p(1 p V(X p X X Z X p N(0, 1 X(1 X/ α P ( Z < z α/ 1 α α P ( Z < z α/ 1 α z α/ 1 (P.45 α 0.05 z α/ , p p 0.9(1 0.9 ( , ( (0.80, z α/ 1 (P.45 P ( X p X(1 X/ < z α/ 1 α P ( X z α/ X(1 X < p < X + z α/ X(1 X 1 α 1 α p X x (x z α/ x(1 x x(1 x, x + z α/ z α/ 1 (P.45 α 0.10 P.106 ( p z α/ p(1 p p(1 p, p + z α/ 7.4 (P (P ( ( , ( (0.593, α p ( p z α/ p(1 p p(1 p, p + z α/ 7.7 (P , α p ( p z α/ p(1 p α P ( Z < z α/ 1 α z α/ α 0.05 z α/ p(1 p, p + z α/ 100, p p 0.95 p 0.67( ( , ( (0.578,

36 8 (P ( 6.1, P.81 ( P σ/ < z α/ 1 α 1 α µ σ σ (X z α/, X + z α/ (a µ X x σ S s p X x (b µ (i σ σ/ N(0, 1 ( P σ/ < z α/ 1 α 1 α µ (X z α/ σ, X + z α/ σ X x σ S/ t( 1 ( P S/ < t α/( 1 1 α 1 α µ (X t α/ ( 1 S, X + t α/ ( 1 S 1 α σ ( 1S ( 1S ( χ X, S x, s α/ ( 1, χ 1 α/ ( 1 S s (ii ( p σ X 1, X,, X i 1,,, X i (µ, σ σ/ N(0, 1 X x σ σ/ N(0, 1 σ S S/ N(0, 1 ( P S/ < z α/ 1 α 1 α µ (X z α/ S, X + z α/ S X, S x, s σ ( *** *** ( 1S σ χ ( 1 ( P χ 1 α/ ( 1 < ( 1S σ < χ α/ ( 1 1 α X p p(1 p/ N(0, 1 p X X p N(0, 1 X(1 X/ 34

37 ( X p P X(1 X/ < z α/ 1 α 8. (P.1 1. H 0 1 α p (X x x(1 x (x z α/, x(1 x x + z α/ µ (a i. σ N(0, 1 ii. σ t( 1 (b ( P ( f(x 1, X,, X R H 0 α i. σ N(0, 1 ii. σ N(0, 1. (σ ( χ ( 1 *** *** 3. p N(0, 1. H 0 3. ( ( H 0 H 0 H 0 R (reject H 0 A (accept T f(x 1, X,, X 1 α (H 0 H 0 β (H 0 H 0 P ( f(x 1, X,, X A H 0 β 1 β (H 0 H 0 P ( f(x 1, X,, X R H 0 1 β 8.1 (P.13 α 0.05, 0.01 H 0 1. µ H 1 H 0 H 0 H 0 1 H 0 ( β ( α (1 β (a i. σ N(0, 1 ii. σ t( 1 (b ( N(0, 1 35

38 . (H 0 : µ 1 µ (a i. σ1 σ N(0, 1 ii. σ1 σ ( N(0, 1 α µ µ 0 ( (b ( 1, ( N(0, 1 3. p N(0, (, P.117 N(µ, σ X 1, X,, X µ X X N(µ, σ X 1, X,, X X σ X N(µ, σ σ/ N(0, 1 (P.81 1 ( 0 σ/ x µ 0 σ/ < z α H 0 : µ µ 0 α H 0 (H 1 H 0 : µ µ 0 H 1 : µ > µ 0 H 0 0 σ/ N(0, 1 P ( 0 σ/ > z α α 0 σ/ x µ 0 σ/ > z α H 0 : µ µ 0 α H 0 (H 1 α µ µ 0 H 0 : µ µ 0 H 1 : µ < µ 0 µ 0 H 0 0 σ/ N(0, 1 P ( 0 σ/ < z α α 8.4 (, P ( H 0 : µ µ 0 H 1 : µ µ 0 H 0 0 σ/ N(0, 1 36

39 P ( 0 σ/ > z α/ α 0.01 H 0 1 α µ (x z α/ σ, x + z α/ σ µ 0 H µ H 0 : µ 604 µ (σ 40, 56 H 0 : µ 616 H 1 : µ < 616 P ( X / 56 < z α α 0 σ/ x / 56 < z α α x µ 0 σ/ < z x µ 0 α/ σ/ > z H 0 α/ α 0.01 H 0 : µ µ 0 x 616 α H 0 (H 1 40/ α µ µ 0 40/ < z α.36 H 1 : µ 604 H 0 : µ 616 H 1 : µ < 616 i X i N(µ, σ (σ 40 X X N(µ, σ σ/ N(0, 1 i X i N(µ, σ (σ 40 X X N(µ, σ σ/ N(0, 1 (σ 40, 56 37

40 H 0 : µ 604 H 1 : µ 604 α 0.05 z α P ( X / α 0.10 z α > z α/ α x 10 0/ / 1.5 < z x / 56 < z x 604 α/ 40/ 56 > z α/ 0.01 H 0 α H 0 α 0.05 x 10 x / 0/ / 1.5 < z / 0.05 H < z α/ 1.96 x H 0 0/ / 1.5 > z H (P (P µ 10 σ m (SIS m ( 18 m 1 %, 5 %, 10 % X i X i N(µ, σ, i 1,,, σ 0, 4 X N(µ, σ σ/ N(0, 1 H 0 : µ 10 H 1 : µ > 10 H 0 X 10 0/ N(0, 1 4 P ( X 10 0/ 4 > z α α α 0.01 z α.36 X 1, X,, X X i N(µ, σ σ/ N(0, 1 H 0 : µ µ 0 H 1 : µ < µ 0 H 0 0 σ/ N(0, 1 P ( 0 σ/ < z α α 38

41 x µ 0 σ/ < z α H 0 : µ µ 0 0 α H 0 S/ (H 1 x µ 0 α µ µ 0 α H 0 (H 1 18 m σ 18 α 0.05 z α , µ , x 80.9 ( x µ 0 σ/ / < z α H 0 : µ µ H 0 H 1 : µ > µ 0 H t ( 0 S/, P.16 N(µ, σ X 1, X,, X X X N(µ, σ 0 S/ σ/ x µ 0 N(0, 1 s/ > t α( 1 H 0 : µ µ 0 α H 0 (H 1 σ σ S α µ µ 0 S/ t( 1 ( 6.5, P.86 1 ( H 0 : µ µ 0 H 1 : µ < µ 0 H 0 0 S/ t( 1 P ( 0 S/ < t α( 1 α s/ < t α( 1 H 0 : µ µ 0 α µ µ 0 t( 1 P ( 0 σ/ > t α( 1 α 3 ( H 0 : µ µ 0 H 1 : µ µ 0 H 0 0 S/ t( 1 P ( 0 σ/ > t α/( 1 α 0 S/ 39

42 x µ 0 s/ < t x µ 0 α/( 1 s/ > t α/( 1 P ( 0 H 0 : µ µ 0 S/ < t α( 1 α α H 0 (H 1 α µ µ 0 x µ 0 s/ < t α( 1 H 0 : µ µ 0 1 α µ (x t α/ ( 1 s, x + t α/ ( 1 s µ 0 H 0 (1 x µ 0 s/ / > t 0.01(4.49 H (P ( 144 x µ 41 (1 0 s/ / > t 0.01 (143 z ( H X 1, X,, X X i N(µ, σ σ/ N(0, 1 σ S S/ t( 1 µ 0 41 α H 0 (H 1 α µ µ (P (1 5 % 3 ( µ µ 95 % 3 H 0 : µ µ 0 H 1 : µ < µ 0 H 0 X 1, X,, X X i N(µ, σ σ/ N(0, 1 σ S 0 S/ t( 1 S/ t( 1 40

43 H 0 : µ µ 0 H 1 : µ µ 0 H 0 0 S/ t( 1 P ( 0 σ/ > t α/( 1 α x µ 0 s/ < t x µ 0 α/( 1 s/ > t α/( 1 H 0 : µ 740 H 0 : µ µ 0 H 0 : µ 630 (H 1 H 0 : µ 690 α H 0 α µ µ 0 (1 α 0.05 t 0.05 ( ( H 0 : µ 740 H 1 : µ 740 x µ 0 s/ / < t 0.05( H 0 H 0 : µ 630 H 1 : µ 630 x µ 0 s/ / < t 0.05( H 0 H 0 : µ 690 H 1 : µ 690 x µ 0 s/ / < t 0.05( H 0 σ σ/ N(0, 1 ( 1 α µ H 0 : µ µ 0 S/ t( 1 P ( σ/ < t α/( 1 α ( 16 P S/ < t α/( 1 1 α α 0.05 t α/ ( α µ (x t α/ ( 1 s, x + t α/ ( 1 s 0.95 µ ( , (63, µ (63, X 1, X,, X E(X i µ, V(X i σ ( 6.1, P.81 X E(X V(X σ/ N(0, 1 σ S 0 σ/ S/ N(0, 1 N(0, 1 (µ µ 0 0 σ/ x µ 0 σ/ 1. H 1 : µ < µ 0 ( 41

44 ( 0 P σ/ < z x µ 0 α α σ/ < z 1 α X 1i N(µ 1, σ1, i 1,,, 1 α H 0 : µ µ 0 X X 1i 1. H 1 : µ > µ 0 ( S1 1 1 (X 1i X 1 ( P σ/ > z x µ 0 α α σ/ > z α α H 0 : µ µ 0 X i N(µ, σ, i 1,,, 3. H 1 : µ µ 0 ( ( P 0 σ/ X 1 X i > z α/ α x µ 0 σ/ > z α/ α H 0 : µ µ 0 S 1 (X i X 1 X 1 X σ S/ N(0, (P (P.57 H 0 : µ µ 0 0 S/ N(0, 1 (µ µ 0 0 S/ x µ 0 s/. H 1 : µ > µ 0 ( ( σ ( 0 (X1 X (µ 1 µ / 1 + σ N(0, 1 P S/ > z x µ 0 α α s/ > z 1 α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 S/ > z α/ α x µ 0 s/ > z α/ α H 0 : µ µ (P.19 E(X 1 X µ 1 µ 4.3 (P (P.59 V(X 1 X σ 1 + σ 1 1. H 1 : µ < µ 0 ( ( 0 P S/ < z x µ 0 α α s/ < z α α H 0 : µ µ 0 X 1 X N(µ 1 µ, σ σ 1 ( H 0 : µ 1 µ H 1 : µ 1 < µ H 0 / σ1 (X 1 X + σ N(0, ( 1 / σ1 P ((X 1 X + σ < z α α 1 4

45 (X 1 X (x 1 x / / ( H 0 : µ 1 µ H 1 : µ 1 > µ σ1 + σ (X 1 X 1 σ1 + σ < z α H 0 : 1 (x 1 x H 0 / σ1 (X 1 X + σ N(0, 1 1 / σ1 P ((X 1 X + σ > z α α 1 (X 1 X / σ1 N(µ + σ 1, 30.5 N(µ, / σ1 (x 1 x + σ > z α H 0 : 1 1 µ 1 µ X 1 X N(µ 1 µ, σ 1 + σ α H 0 (H 1 1 α µ 1 µ ( (X 1 X (µ 1 µ 3 ( H 0 : µ 1 µ H 1 : µ 1 µ H 0 / σ1 (X 1 X + σ N(0, σ < z α/ µ 1 µ 1 α H 0 (H 1 / σ α µ 1 µ 1 (x 1 x + σ > z α/ 1 / σ 1 / σ σ H 0 : µ 1 µ α H 0 (H 1 α µ 1 µ 8.6 (P % H 0 : µ 1 µ H 1 : µ 1 > µ / σ σ N(0, 1 H 0 / σ1 (X 1 X + σ N(0, 1 1 / σ1 P ( X 1 X + σ > z α/ α 1 / σ1 P ((X 1 X + σ > z α α 1 43

46 / σ1 (x 1 x + σ > z α H 0 : 1 S1 1 1 (X 1i X µ 1 µ α H 0 (H 1 S 1 (X i X α µ 1 µ 1 α 0.05 z α x 1 64, x 56, σ1 30.5, σ 75.6, 1 5, 9 / 8.6. ( 1,, P X 1i N(µ 1, σ 1, i 1,,, 1 X 1 X i N(µ, σ, i 1,,, α H 0 (H 1 X α µ 1 µ 1,, X 1 X s (x 1i x / σ1 X 1 X + σ N(0, 1 1 t σ1 (x 1 x + σ 1 ( 1 / H 0 : µ 1 µ 30.5 ( H 1 : µ 1 < µ 9.10 > z H 0 H 0 / (X 1 X S S N(0, 1 / S1 P ((X 1 X + S < z α α 1 (X 1 X (x 1 x / / σ1, σ S 1, S 1, ( 6.1, P.81 ( / S1 X 1 X + S H 0 : µ 1 µ N(0, 1 1 H 1 : µ 1 > µ S S s 1 + s < z α H 0 : 1 µ 1 µ s 1 1 (x i x 44

47 H (P.13 / S 1 (X 1 X + S N(0, 1 1 / S1 P ((X 1 X + S > z α α 1 (X 1 X / S1 + S 1 1 1, / s 1 (x 1 x + s > z α H 0 : 1 X 1 X N(µ 1 µ, S 1 + S 1 µ 1 µ α H 0 (H 1 ( / (X 1 X (µ 1 µ α µ 1 µ 3 ( H 0 : µ 1 µ H 1 : µ 1 µ H 0 / / S1 (X 1 X + S S N(0, 1 1 (X 1 1 X + S N(0, 1 1 / S1 P ( X 1 X + S > z α/ α 1 (X 1 X / S1 + S 1 (X 1 X / / s s 1 (x 1 x + s 1 (x 1 x + s > z α H 0 : < z α/ 1 1 µ 1 µ / s α H 0 (H 1 1 (x 1 x + s > z α/ α µ 1 1 µ H 0 : µ 1 µ α H 0 (H 1 α 0.05 z α α 0.01 z α.36 α µ 1 µ 10 1 %, 5 % H 0 : µ 1 µ H 1 : µ 1 > µ S S N(0, 1 H 0 1, / S1 P ((X 1 X + S > z α α 1 / S S x 1 615, x 606, s 1 40, s 3, 1 154, 45

48 / s 1 (x 1 x + s 1 / 40 ( > z Z X E(X 0.05 H 0 V(X/.07 > z ( 0.01 H 0 H 0 : p p 0 H 1 : p < p 0 X X 1, X,, X ( 6.1, P.81 p(1 p E(X p, V(X X p p(1 p/ N(0, (P.136 ( i X i 1 X i 0 R X i R 1 p P (X i 1 p X i E(X i 1 P (X i P (X i 0 p V(X i (1 p P (X i 1 +(0 p P (X i 0 p(1 p H 0 X p 0 N(0, 1 p0 (1 p 0 / X p 0 P ( p0 (1 p 0 / < z α α X p 0 p0 (1 p 0 / x p 0 p0 (1 p 0 / < z α H 0 : p p 0 α H 0 (H 1 α p p 0 p p 0 p0 (1 p 0 / < z α α p p 0 P (4.1 ( (4.14 H 0 : p p 0 p X H 1 : p > p 0 X R 1 X i ( p X p E(X 1 E(X E(X p V(X 1 V(X V(X p(1 p H 0 X p 0 N(0, 1 p0 (1 p 0 / X p 0 P ( p0 (1 p 0 / > z α α 46

49 X p 0 p0 (1 p 0 / 170 x p 0 p0 (1 p 0 / > z α H 0 : p p 0 α H 0 (H 1 X p Z N(0, 1 α p p 0 p(1 p/ p p 0 p0 (1 p 0 / > z α α p p 0 3 ( H 0 : p p 0 H 1 : p p 0 H 0 X p P ( 0 X p p0 (1 p 0 / > z α α 0 N(0, 1 p0 (1 p 0 / X p 0 p0 (1 p 0 / X p 0 P ( p0 (1 p 0 / > z α/ α x p 0 p0 (1 p 0 / > z α H 0 : p p 0 α H 0 (H 1 X p 0 p0 (1 p 0 / α p p 0 x p0 p0 (1 p 0 / < z p p 0 α/ p0 (1 p 0 / > z p α/ α 0.05 z α H 0 : p p , x α H 0 (H 1 x p 0 α p p 0 p p 0 p0 (1 p 0 / < z α/ p p 0 p0 (1 p 0 / < z α/ α p p 0 H 0 : p p 0 H 1 : p > p 0 H 0 X p 0 N(0, 1 p0 (1 p 0 / p0 (1 p 0 / > z α 0.109( / H % 47

50 ( µ X 1 X i x 1 x i σ S 1 (X i X s 1 (x i x 1 1 p (? X R 1 X i x 1 x i ( p {X 1, X,, X } {x 1, x,, x } R x X S X µ {X 1, X,, X } i 1,,, X i N(µ, σ σ ( σ/ N(0, 1 P σ/ < z α/ 1 α z α/ 100 α % α (P.45 σ σ P (X z α/ < µ < X + z α/ 1 α σ σ X x 1 α µ (x z α/, x + z α/ σ ( S/ t( 1 P S/ < t α/( 1 1 α t α/ ( α % α 1 t (P.47 P (X t α/ ( 1 S < µ < X + t α/ ( 1 S 1 α ( X, S x, s 1 α µ x t α/ ( 1 s, x + t α/ ( 1 s 48

51 (, {X 1, X,, X } i 1,,, X i (µ, σ ( σ ( 6.1, P.81 ( σ/ N(0, 1 P σ/ < z α/ 1 α σ σ P (X z α/ < µ < X + z α/ 1 α σ σ X x 1 α µ (x z α/, x + z α/ σ σ S σ/ N(0, 1 ( S/ N(0, 1 P S/ < z α/ 1 α S S P (X z α/ < µ < X + z α/ 1 α ( X, S x, s s s 1 α µ x z α/, x + z α/ σ ( p X p p(1 p/ N(0, 1 p X X p ( X p N(0, 1 P X(1 X/ X(1 X/ < z α/ 1 α ( X(1 X X(1 X P X z α/ < p < X + z α/ 1 α ( x(1 x x(1 x X x 1 α p x z α/, x + z α/ 49

52 ( µ {X 1, X,, X } i 1,,, X i N(µ, σ σ X σ/ N(0, 1 H 0 : µ µ 0 0 σ/ N(0, 1 (µ µ 0 0 σ/ x µ 0 σ/ 1. H 1 : µ < µ 0 ( ( 0 P σ/ < z x µ 0 α α σ/ < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P σ/ > z x µ 0 α α σ/ > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 σ/ > z α/ α x µ 0 σ/ > z α/ α H 0 : µ µ 0 σ X S/ t( 1 H 0 : µ µ 0 0 S/ t( 1 (µ µ 0 0 S/ x µ 0 s/ 1. H 1 : µ < µ 0 ( ( 0 P S/ < t x µ 0 α( 1 α s/ < t α( 1 α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P S/ > t x µ 0 α( 1 α s/ > t α( 1 α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 S/ > t α/( 1 α x µ 0 s/ > t α/( 1 α H 0 : µ µ 0 ( {X 1, X,, X } i 1,,, X i (µ, σ ( 50

53 σ σ/ N(0, 1 H 0 : µ µ 0 0 σ/ N(0, 1 (µ µ 0 0 σ/ x µ 0 σ/ 1. H 1 : µ < µ 0 ( ( 0 P σ/ < z x µ 0 α α σ/ < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P σ/ > z x µ 0 α α σ/ > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 σ/ > z α/ α x µ 0 σ/ > z α/ α H 0 : µ µ 0 σ S/ N(0, 1 H 0 : µ µ 0 0 S/ N(0, 1 (µ µ 0 0 S/ x µ 0 s/ 1. H 1 : µ < µ 0 ( ( 0 P S/ < z x µ 0 α α s/ < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( 0 P S/ > z x µ 0 α α s/ > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( P 0 S/ > z α/ α x µ 0 s/ > z α/ α H 0 : µ µ 0 (H 0 : µ 1 µ 1 1 i 1,,, X 1i N(µ 1, σ1 i 1,,, X i N(µ, σ σ1 σ X 1 X 4.1 (P (P.57 E(X 1 X µ 1 µ 4.3 (P (P.59 V(X 1 X σ 1 + σ X 1 X N(µ 1 µ, σ 1 + σ (

54 (X 1 X (µ 1 µ X 1 X N(0, 1 H 0 : µ 1 µ σ1 / 1 + σ / σ 1/ 1 + σ / N(0, 1 X 1 X x 1 x (µ 1 µ 0 σ 1/ 1 + σ / σ 1/ 1 + σ / 1. H 1 : µ 1 < µ ( ( X 1 X P σ 1/ 1 + σ / < z α α x 1 x σ 1/ 1 + σ / < z α α H 0. H 1 : µ 1 > µ ( ( X 1 X P σ 1/ 1 + σ / > z α α x 1 x σ 1/ 1 + σ / > z α α H 0 3. H 1 : µ 1 µ ( ( X 1 X P σ1/ 1 + σ/ > z α/ α x 1 x σ1/ 1 + σ/ > z α/ α H 0 σ1 σ ( t ( 1, 1 1 i 1,,, X 1i (µ 1, σ1 ( i 1,,, X i (µ, σ ( σ1 σ (X 1 X (µ 1 µ σ1 / 1 + σ / N(0, 1 H 0 : µ 1 µ X 1 X X 1 X σ 1/ 1 + σ / N(0, 1 (µ 1 µ 0 σ 1/ 1 + σ / x 1 x σ 1/ 1 + σ / 1. H 1 : µ 1 < µ ( ( X 1 X P σ 1/ 1 + σ / < z α α x 1 x σ 1/ 1 + σ / < z α α H 0. H 1 : µ 1 > µ ( ( X 1 X P σ 1/ 1 + σ / > z α α x 1 x σ 1/ 1 + σ / > z α α H 0 5

55 3. H 1 : µ 1 µ ( ( X 1 X P σ1/ 1 + σ/ > z α/ α x 1 x σ1/ 1 + σ/ > z α/ α H 0 σ1 σ (X 1 X (µ 1 µ S1 / 1 + S / N(0, 1 H 0 : µ 1 µ X 1 X X 1 X S 1/ 1 + S / N(0, 1 (µ 1 µ 0 S 1/ 1 + S / x 1 x s 1/ 1 + s / 1. H 1 : µ 1 < µ ( ( X 1 X P S 1/ 1 + S / < z α α x 1 x s 1/ 1 + s / < z α α H 0. H 1 : µ 1 > µ ( ( X 1 X P S 1/ 1 + S / > z α α x 1 x s 1/ 1 + s / > z α α H 0 3. H 1 : µ 1 µ ( ( X 1 X P S1/ 1 + S/ > z α/ α x 1 x s 1/ 1 + s / > z α/ α H 0 p X p N(0, 1 H 0 : p p 0 p(1 p/ X p 0 N(0, 1 p0 (1 p 0 / (p p X p 0 0 p0 (1 p 0 / x p 0 p0 (1 p 0 / 1. H 1 : µ < µ 0 ( ( X p 0 P p0 (1 p 0 / < z α α x p 0 p0 (1 p 0 / < z α α H 0 : µ µ 0. H 1 : µ > µ 0 ( ( X p 0 P p0 (1 p 0 / > z α α x p 0 p0 (1 p 0 / > z α α H 0 : µ µ 0 3. H 1 : µ µ 0 ( ( X p 0 P p0 (1 p 0 / > z x p 0 α/ α p0 (1 p 0 / > z α/ α H 0 53

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