第八章 統計估計

t

(statistical inference)

(point estimator)

(interval estimator)(point estimator)

0(interval estimator)525 (n=25) $400

$380 $420

(unbiasedness)(consistency)(relative efficiency)

1. (unbiased estimator) (biased estimator) 2

2.

(consistent)

3. (relatively more efficient)

3. MeMe

/

Me

12

2: (1)

2: (2)

n=3 21 n=4 1 2 n>4 1 23 2

3: (1)

2

3: (2)

2

(interval estimate) (margin of error)

() ()

(interval estimator)

( ___% ) 3.() (1) (X1X2. . . . . . Xn)f(x) nT1T2 P( T1T2)=1- (T1, T2) 100(1-) %1-(confidence level)(2) d 100(1-)%

3.-

() (1) (i)!! nn>30 100(1-)%

()

()

n>30

100(1-)%

3.-

(ii)!!nn>30dn

()

3.- ) n>30

100(1-)%

()

(i) )

(Lower confidence limit) =

(Upper confidence limit) =

1

3.-3.-(ii) ( n>30) n>30 S2 2

100(1-)%

()

3.-(iii) () (a) 100(1-)%

(b) 100(1-)%

3.-(iv) ( n302

95%

4. (c)25695% n=2530 p

p100(1-)%

3.p-

(ii)!! nn>30dn (a)

(b) p

4.p-n>30 np 5 n(1p) 5)

()

p100(1-)%

4.p

6. 900 396 396/9000.44 n=900>30 p

p95%

95% p (0.4076, 0.4724 ) 95% 40.76% 47.24%

7. 0.0195 7. p p=1/2

9,604

5.2-

() 22 2 2 2

5.2- 2

2100(1-)%(

8.23 0 =18,540295% 22 100(1-)%

2 100(1-)%

9. 2295%ABCDE5040305260n55468

2 2 100(1-)%

2 95%

6. 1-2 1 2 2 21n1 2n2 12n1 n2 30

6. 1-2(1)

() (12) 1-21-2

6. 1-2(1)

()(12)1-2 1-2

1-2100(1-)%

10. 1 2

G12

10. 1 2

19 210Greystone

95%

n1=36, n2=49>3019 , 210 1 - 2

95% z/2z0.0251.961 - 295%

6. 1-2(2)

() (12n1 n2) 1-212n1 n2 (30) , 1-2

6. 1-2(2)

()(12n1 n2)1-2 1-2

1-2100(1-)%

6. 1-2(3)

() (121=2=n1 n2) 1-2121=2=

1-2 t

6. 1-2(3)

()(121=2=n1 n2)1-2 1-2

1-2100(1-)%

11 . 121=2=

AB

95%

A35401,80020,000B40388,00022,000

n1=36, n2=49>31 2

n1=36, n2=49 1-2

95% t/2z0.0251.961 - 295%

6. 1-2(4)

() (121=2 n1 n2) 1-2121=2

6. 1-2(4)

() (121=2 n1 n2)1-2 t

ta/2

6. 1-2(4)

()(121=2 n1 n2)1-2 1-2

1-2100(1-)%

12 .121=2 Cherry Grove28Beechmont22

12. 121=2 ClearwaterCherry GroveBeechmont95%: Cherry Grove n128, $1,025 s1$150Beechmont n222, $910, s2$125t/2

47 t t47 t0.025,472.01295%

95%(37, 193)

6.1-2(5) 1 2 2 2paired samples

6.1-2(5)

776.1-2(5)

() () (D1D2. . . . . . Dn) 1-2(!!)

6.

6.

()

13 .13.

13. n=7