CH6-1 Estimation.pdf

1

6

2

P

P

2

X

S

2

6.1

2

(Point Estimation)

(Interval Estimation)

3

(Estimator)

a b

a b

4

1. (Unbiaseness) 2. (Consistency) 3. (Sufficiency) 4. (Minimum Variance)

6.1.1

5

X1, X2, , Xn n

6.1.2 1

2

7

a b

a b (1-)100%

8

3 1) 2) 3)

1

1)

9

n

XZ

2

10

/2 /2

XP z z 1

n

/2 /2P X z X z 1n n

/2 /2P z Z z 1

11

n (1-)100%

2 2

x z x zn n

2)

12

XZ

S n

2

2S2

13

(n 30) (1-)100%

2 2

s sx - z x z

n n

2

3)

14

T t n-1

nS

XT

2

15

1n

stX

n

st-XP

1tnS

Xt-P

22

22

t

16

(1-)100%

2 2

s sx - t x t

n n

n n< 30 2

6.1 36 2.6 0.3 99%

17

2,n-1 2,n-1

s sx - t x t

n n

18

95%

95% /

19

6.2 49 48.5 2.2 90%

20

95%

90%

22

23

6.1.3 2

2

n1 1

n2 2

111 12 1nX ,X , ,X

1111 12 1n

X ,X , ,X

2

1

2

2221 22 2n

X ,X , ,X

2

1 2

24

21 XX

21 -

1:

2:

1X

2X

1

2

a b (1- )100%

25

1 2a b

1 2P a b 1

2. n1 n2

3. n1 n2

1.

2

2

2

1 ,

2

2

2

1 ,

4 n1 n2

2

2

2

1 ,

2

2

2

1 ,2

2

2

1

2 21 2

27

21 nn

)()XX(Z

2

2

2

1

2121

1) ,

2

12

2

28

(1 )100%

2 2 2 2

1 2 1 2

1 2 1 2 1 2

1 2 1 22 2

x x z x x zn n n n

29

2) n1 n2

2

2

2

1 ,

21 nSnS

)()XX(Z

2

2

2

1

2121

30

(1-)100%

2 2 2 2

1 2 1 2S S S S

1 2 1 2 1 2

1 2 1 22 2

x x z x x zn n n n

31

3) n1 n2

2

2

2

1 ,2 2

1 2

t n1 + n2 - 2

1 2 1 2

2

p

1 2

(X X ) ( )T

1 1S ( )n n

32

(1 )100%

2 2

2 1 1 2 2p

1 2

(n 1)S (n 1)SS

n n 2

1 2 p 1 2 1 2 p1 2 1 22 2

1 1 1 1x x t s x x t s

n n n n

4) n1 n2

33

2

2

2

1 ,2

2

2

1

21 nSnS

)()XX(T

2

2

2

1

2121

t 2 21 2

2 2

1 2

2

1 2

2 2

1 2

1 2

[s n s n ]v

(s n ) (s n )

n 1 n 1

T

34

(1 )100%

2 2 2 2

1 2 1 2S S S S

1 2 v 1 2 1 2 v

1 2 1 2

x x t x x tn n n n

2 21 2

2 2

1 2

2

1 2

2 2

1 2

1 2

[s n s n ]v

(s n ) (s n )

n 1 n 1

6.3 A B A 75 B 80 A 6,800 600 B 4,450 500 90%

35

= A

= B

- ?

- ?

- ?

1

2

36

90%

37

2 2 2 2

1 2 1 2S S S S

1 2 1 2 1 2

1 2 1 22 2

x x z x x zn n n n

6.4 Serum amylase 15 Serum amylase 96 unit/100ml 35 unit/100ml 22 Serum amylase 120 40 unit/100ml 95 % Serum amylase

38

=

=

1

2

39

95%

40

6.5 A B A B 10 16 A 120 25 B 112 20 A B 95% A B

41

A B

= A

= B

- ?

- ?

- ?

1

2

42

1 2

95%

-1:

-2:

43

2 2 2 2

1 2 1 2S S S S

1 2 v 1 2 1 2 v

1 2 1 2

x x t x x tn n n n

1 2

2 2

1 2

2 2

1 2

2

1 2

2 2

1 2

1 2

[s n s n ]v

(s n ) (s n )

n 1 n 1

44

6.1.5 p

p n

XP

n p pq/n

X n p

P

45

n

pq

pPZ

pq

pq

5

46

(1-)100% (p)

2 2

pq pq p z p p z

n n

6.7 500 160 95%

47

95%

49

50

6.1.6

2 p1 - p2

p1 - p2

p1 - p2 1 1 2 2

1 2

p q p q

n n

21 PP

51

n1 n2

2

22

1

11

2121

n

qp

n

qp

)p(pPPZ

p1q1 p2q2 1 1 p q 2 2 p q

5

52

2

(1 )100%

1 1 2 2 1 1 2 21 2 1 2 1 21 2 1 22 2

p q p q p q p q p p z p p p p z

n n n n

53

6.8 400 600 100 300 95%

=

=

54

1 1 2 2 1 1 2 21 2 1 2 1 21 2 1 22 2

p q p q p q p q p p z p p p p z

n n n n

90%

55

56

6.1.

S2

2

22

1)S(n

n-1

2

5

57

1

1)S-(n

1)S-(nP

1

1)S(nP

1P

2

/21

22

2

2

2

2

22

/21

2

22

/21

58

(1 )100%

2

/21

22

2

/2

2

1)S-(n

1)S-(n

59

6.8 10

16.4 , 16.1 , 15.8 , 17.0 , 16.1 , 15.9 , 15.8 , 16.9 , 15.2 16.0

95%

95%

61

62

6.1.8 2

2 2221 2221 SS

2

2

2

2

2

2

1

2

1

S

SF

F F v1 = n1-1 v2 = n2-1

5

63

1 2 1 2

1 2 1 2

1 2 1 2

1 /2, v ,v /2, v ,v

2 2

1 21 /2, v ,v /2, v ,v2 2

1 2

2 2 2

1 1 1

2 2 2

2 2 2/2, v ,v 1 /2, v ,v

P f F f 1

S SP f f 1

S S1 1P 1

S f S f

64

2

(1 )100%

1 2 1 2

2 2 2

1 1 1

2 2 2

2 2 2/2, n 1,n 1 1 /2, n 1,n 1

S S1 1

S f S f

1 2

2 1

(1 /2),(n 1,n 1)

( /2),(n 1,n 1)

1f

f

2 1

1 2

2 2 2

1 1 1/2, n 1,n 12 2 2

2 2 2/2, n 1,n 1

S S1f

S f S

6.9 21 Parkinson 16 1,600 ()2 Parkinson 1,225 ()2 95%

65

=

=

66

2 1

1 2

2 2 2

1 1 1/2, n 1,n 12 2 2

2 2 2/2, n 1,n 1

S S1f

S f S

95%

67

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CH6-1 Estimation.pdf