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http://www.easymr.com

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• 

 

 

• Statistics: the science of 

collecting, analyzing, 

presenting, and 

interpreting data. 

• Copyright 1994-2000 Encyclopaedia Britannica, Inc. 

• 

 


1. 107100 

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1/216 

1/6 

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1 

1 

2 

1 

1 

) 

( 

&

(degree of freedom) 

1. 

2. n ⎯x 

n-1 

 

3. 3x 1 

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5 ⎯x = 5 x 1 

x 2 

x 3 

 

x 1 

=6x 2 

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x 3 

2 

4. 

 

2 2 

 


• 

• 

• 

• 

• 

X 

− 

X 

Z 

= 

i 

i 

σ 

x 

− 

x 

 

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= 

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S 

n 

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σ 

s 

X 

= 

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x 

 



( 

) 

 

 

 

 

(%) 

25 

20 

15 

10 

1. 

 

2. 

5 

500 

1000 

1500 2000 2500 3000 3500 4000 4500 5000 

 

() 

 


• 

• 

• 

• 

• 

• T 

 


1. 

• 

• “” 

 

• 

• 

2. 

• 

• 

3. 

 

 


N ~ ( (, 2 ) 

n 

⎯X⎯X 

 

2 /n⎯XN(, 2 /n) 

σ =10 

n = 4 

σ = =55 

σ x 

n =16 

σ =2.5 5 

σ x 

µ = 50 

 

X 

µ x 

µ = =50 

 

X 

 


µσ 2 

n 

n 

 

2 /n 

σ 

x 

σ 

= 

n 

 

(n ≥ 30) 

 

 

 

 

µ x = µ 

X 

x = 


N ~ ( (, 2 ) X 1 

X 2 

…X n 

 

s 2 

2 

( n 

− 

1) 

s 

2 

~ 

χ 

( 

n 

− 

1) 

2 

σ 

χ 2 (n – 1) 

(n-1) 1) 

 


• 

 

• 

• 

σ = 

x 

σ 

n 

 


(χ 2 ) 

 

µ 

σ 

n 

 

S 2 

 

χ 2 = (n-1)S 2 / 2 

 

χ 2 

 

n=1 

n=4 

n=10 

n=20 

χ 2 

 


T 

X 1 

X 2 

…X n1 N~( 

~( 1 

, 

2 

1 

) 

 

n 

( X 

− 

µ) 

T 

= 

, 

(n-1) 1)t 

S 

t 

 

t (df 

= 13) 

 

t 

 

X 

t 

t (df 

= 5) 


Z 

t

. 

. 

 

 


µ x 

P pˆpˆ 

σ 

2 s 

2 

1 µ 

2 x 1 − 

x 

2 

1 

p ˆ 

1 − 

p 

ˆ 

P 

2 

2 

2 

2 

2 

2 

2 

s 1 s 

2 

µ − 

2 

P − 

2 

σ 1 σ 

 


1. 

 

• : 

 

2. 

 

3. 

 

 


• 

 

P( X ) 

 

 

A 

C 

µ 

X 

 


P(X ) 

 

B 

A 

 

µ 

X 

 


• 

 

P(X ) 

 

B 

A 

 

µ 

X 

 


• 

• 

• : 50~70 95% 

 

 

() 

 

 

 


X = µ ± Zσ x 

σ x 

_ 

µ 

µ - 2.58σ x µ -1.65 

σ x µ +1.65σ x µ + 2.58 x 

µ -1.96 

σ x µ +1.96σ x 

X 

 

90% 

95% 

99% 


1. 

2. (1 - α) % 

α 

3. 99%, 95%, 90% 

α 0.010.050.10 

 


• 

 

 

• p 

• 

Sp 

• n 

• z0.951.96z0.992.58 

• 95% 

x 

x 1. 96s x 

S x 

p ±1. 96s 

± p 

 


(σ ) 

1. 

– σ 

– 

2. t 

t 

= 

s 

x 

− 

µ 

n 

− 

1 

n 

~ 

t 

( 

n 

− 

1) 

3. µ 1-α 

 

⎛ 

⎜ 

⎝ 

x 

− 

t 

s 

x 

+ 

n−1 

n−1 

α 2 

, 

α 2 

n 

t 

s 

n 

⎞ 

⎟ 

⎠ 

 


n = 25 

⎯x = 

50 

s = 88 

 

µ 

95% 

 

 

~N(µσ 2 )⎯x=50, 

s=8 

n=25, 1-α 1 = 0.95t α/2 /2=2.0639 

⎛ 

s 

n 

− 

1 

s 

n 

− 

1 

⎞ 

⎜ 

x 

− 

t 

α 

2 

, 

x 

+ 

t 

α 

2 

⎟ 

⎝ 

n 

n 

⎠ 

⎛ 

= 

⎜ 

50 

− 

⎝ 

= 

2.0639 

( 46.69,53.3 

) 

8 

,50 

+ 

25 

8 

⎞ 

2.0639 

⎟ 

25 

⎠ 

95 

95 

46.6953.30 

 

 


1. 

 

– 

– 

– 

2. 

Z 

= 

p 

ˆ 

− 

p 

p 

(1 

− 

p 

) 

~ 

N 

(0,1) ) 

n 

3. 

p 

p 

ˆ (1 

− 

± Z 

α 

n 

ˆ ± α 2 

p 

ˆ ) 


200 

200 

 

140 

140 

 

 

 

 

 

95% 

 

p ∧ 

 

n=200 

0.7 

, n =140= 

140>5, 

n(1- p ∧ 

)=60>5α= = 0.95 α/2 /2=1.96 

p 

ˆ 

(1 

− 

p 

ˆ 

) 

p 

ˆ ± 

Z 

α 

2 

n 

= 

0.7 

± 

1.96 

( 0.636 

,0.764 

) 

p ∧ 

0.7(1 

− 

0.7) 

200 

95 

95 

 

63.6%~76.4% 

63.6%~76.4% 


1. n 

2 

Z α 

2 

σ 

n = 

2 

∆ 

2 

∆ 

2 

 

Z 

∆ = 

α 2 

2. n 

σ 2 ∆ 

Z 

 

• 

• 

• 

σ 

n 

 


1800000 

95% 

 

 

500 

 

 

 

 

 

: σ 2 =1800000 α =0.05 

Z α/2 /2=1.96∆=500=500 

 

n 

= 

= 

= 

2 

Z α 

2 

σ 

2 

2 

∆ 

2 

(1.96 ) 

(1800000 

2 

500 

27 .65 

≈ 

28 

) 


1. n 

n 

2 

Z 

α 

2 p 

(1 

− 

p 

) 

= 

2 

∆ 

 

∆ = Z 

α 

n 

p 

(1 

− 

p 

) 

2. P 

2 

p^ 

 

 



 

 

 

 

: 

∆=0.05 

=0.05α=0.05 

=0.05Z α/2 

/2=1.96 

=1.96 

 

p 

0.25 

0.25 

 

^ 

 

 

 

385 

(0.5) 

0.5) 

(0.5)(1 

(1.96 ) 

) 

(1 

2 

2 

2 

2 

2 

≈ 

− 

= 

− 

= 

∆ 

α 

p 

p 

Z 

n 

385 

(0.5) 

0.5) 

(0.5)(1 

(1.96 ) 

) 

(1 

2 

2 

2 

2 

2 

≈ 

− 

= 

− 

= 

∆ 

α 

p 

p 

Z 

n 

• 

 

 

 

 

p 

 

0.05 

95% 

 

 

p

• 

• 

• 

• P 

 


... 

... 

µ = 50 

... 

 

 

20 

µ = 50 

H 0 

 


☺ ☺ 

☺ 

☺ 

☺ 

☺ 

☺ 

 

 

 

 

 

! 

. 

 

☺ 

 

⎯X = 20 

☺ 


• 

– 

– 

– 

– 

– 

 


Z 

t 

Z 

χ 2 

 

 

 

 

 


P P-Value 

Value 

• 

• P- 

(< > 

– P- 

 

– P- 

 

• () 

– H0 α 

 


(χ 2 ) 

• 

• CROSSTABS 

• 

• SPSS 

• / 

 

 

 

 

, , 

 

 


* Crosstabulation 

Pearson Chi-Square 

Continuity Correction 

Likelihood Ratio 

Fisher's Exact Test 

Linear-by-Linear Association 

N of Valid Cases 

a. Computed only for a 2x2 table 

a 

Count 

 

 

Total 

Value 

 

 

Chi-Square Tests 

3.243 b 1 .072 

1.441 1 .230 

4.402 1 .036 

3.162 1 .075 

40 

df 

 

Total 

 

20 0 20 

Asymp. Sig. 

(2-sided) 

b. 2 cells (50.0%) have expected count less than 5. The minimum expected count is 1.50. 

17 3 20 

37 3 40 

Exact Sig. 

(2-sided) 

 

 

 

 

 

 

Exact Sig. 

 

(1-sided) 

 

 

0 

.231 .115 


20317 

 

, 

Fisher

• 0%0/20, 

15%3/20 

 

0% 

, 

 

 

 

 

• 

 

 

 

 

 

 

 


1. 

 

 

 


• 

0 

 

• 

 

 

 

 


T 

• 

 

30 

t 

z 

• t 30 

30 

t 

t 

t 

 

• 

 

 

t 

 

 


• 

 

 

• 

 

 

 


n 

---- 

---- 

TV 

 

 

TV 

TV = 

∑∑( x x ) 

ij 

− 

TVxk 

x 

j 

k 

n 

j 

j= 1 i= 

1 

2 

ij 

ji 

 


---- 

---- 

VB 

 

 

VB 

= 

k 

∑ 

j= 

1 

n 

( x 

VBx 

kn 

j 

x 

x 

j 

j 

− 

2 

) 

ij 

j 

 


---- 

---- 

VW 

 

 

VW = 

x 

( x − x ) 

VWk, 

n 

ij 

k 

n 

j 

∑∑ 

j= 1 i= 

1 

ij 

jix 

j 

2 

j 

j 

j 

 

 


• 

• 

• 

 

 

 


F 

F 

 

 

• 

 

• 

• 

 

 

 

 


• 

 

 

 

 

• 

 

 

 

 

 


• 

• 

• 

•

N - 中国经济学教育科研网

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