6.1抽样调查（课件）《统计学》（航空工业出版社）

三、抽样调查中的基本概念

样

本

概念全及指标样本指标

单位数目Nn

平均数

Xx

成数PP

方差σ2S2

标准差σS

XXF

XX

NF

PN1

N

2

2

XXXXF

XσX

σNF

P(1P)

σP

22

XXXXF

σX

NσXF

P(1P)

P

N

P1

N

XFN1

XP

FN

22

XXxxxxF

22

1P1PN1

22

1PN1PN0

2

22

xxfPN01PN1

σ

fN

22

PN1PN2

01P2Q1PP

NN

P2QQ2PPQPQPQP1P

0.9510.9521.79%.

xxf

xx

nf

pn1

n

22

xxf

xx

σX

σXnf

p(1p)

σP

22

xxf

xx

σX

σXnf

p(1p)

P

N!

An

NNn!

nn

BNN

N!

Cn

Nn!Nn!

nn

DNCNn1

2

xxXxX

2

xx3.3334

抽样平均误差0.58

n10

σ2σ

μ

xnn

σ2p(1p)

μpnn

σ2n

1

μxnN

p1pn

μ1

pnN

s2p

计算例题：

22

xxx(xx)(xx)f

xf552.5

x5.5安培

f100

2

xxf19.25

s0.4387安培

f100

s0.4387

μ0.04387安培

xn100

σ2n0.43872100

μ110.04385安培

xnN10010000

n1005

p195%

n100

p1p0.9510.95

μ2.179%

pn100

p1pn0.9510.95100

μ112.178%

pnN10010000

t

Δxμx

t

Δpμp

μ3σxμ3σx

t

Δxμx

t

Δxμx

t

Δpμp

t

Δpμp

xXpp

XxΔx

MNXNxΔx

PpΔp

WNPNpΔp

2

fxxfxxf

xf1250

x5小时

f250

2

xxf1136

s2.13小时

f250

s2.13

Δtμ20.130.26小时

μ0.13小时xx

xn250

XxΔ50.264.76-5.26小时

x

n30台,x4.5万小时

s240小时Ft95%t1.96

Δ?

xX?

s240

μ43.80小时

xn30

Δtμ1.9643.8085.84小时

xx

XxΔ4.51000085.84

x

44914.16-45085.84小时

22

xxxxxxxf

（米）

2

xf33.6xxf0.648

x1.12米s20.0216米

f30f30

s20.0216

μ0.0268米

xn30

Δtμ1.960.02680.0526米

xx

XxΔ1.120.05261.0674-1.1726米

x

n1

n200件

n18件N20Ft95%

t1.96

P?

n8

p14%

n200

p1pn0.0410.041

μ111.35%

pnN20020

t=1.96×1.35%=2，.65%

Δpμp

ppΔp4%2.65%1.35%~6.65%

p(1p)0.6510.65

μ4.77%

Pn100

ΔPtμp1.964.77%9.35%

PPΔp65%9.35%55.65%~74.35%

已知:N100万,n1000,n120,Ft99.73%,t3

求:P?

n20

解:(1)p12%

n1000

p1p0.0210.02

(2)μ0.4427%

pn1000

(3)Δptμp30.4427%1.33%

(4)PpΔp2%1.33%0.67%~3.33%

n400户n187户

Δp3.88%

P?Ft?

n87

p121.75%

n400

PpΔp21.75%3.88%17.87%~25.63%

Δ

t∴p

Δpμpt

μp

p1pn21.75%121.75%400

μ111.98%

pnN4005000

Δp3.88%

∴t1.96%

μp1.98%

Ft95即%：这一估计的可靠程度为95%。

t2σ2

nx2

Δx

t2P1P

………

np2

Δp

Nt2σ2

n

x222

NΔxtσ

Nt2P1P

………

np22

NΔptP1P

已知：p6%,Δp0.02,F(t)0.9973,t3,

求：n?

t2p(1p)

解：n2

Δp

326%(16%)0.5076

1269(件)

0.0220.0004

答：以0.9973的概率保证，最少抽取1269件。

Δp3%Ft95%t1.96P189.15%

P289.50%P390.10%

np?

22

tP1P（1）1.960.891510.8915

np22413棵

Δp0.03

n100瓶δ3片

x101.5片x

Ft99.73%t3

X?

/1

ΔΔn?

x2xx

s3

μ0.3片

xn100

Δxtμ