báo cáo xác suất thống kê

7/27/2019 Bo co xc sut thng k

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BI TP LN XC SUT THNG K GVHD: GS.TS NGUYN NH HUY

THI QUANG THNHG1003223 1

BI 1:

Cu 1:(V d 3.4/207/Gio trnh XSTKGS-TS Nguyn nh Huy)

Hiu sut phn trm (%) ca mt phn ng ho hc c nghin cu theo ba yu t pH

(A), nhit (B) v cht xc tc (C) c trnh by trong bng sau:

Yu tA

Yu t BB1 B2 B3 B4

A1 C1 9 C2 14 C3 16 C4 12A2 C2 12 C3 15 C4 12 C1 10A3 C3 13 C4 14 C1 11 C2 14A4 C4 10 C1 11 C2 13 C3 13

Hy nh gi vnh hng ca cc yu t trn hiu sut phn ng?Giis

DNG TON:

Phn tch phng sai ba yu t.

C S L THUYT:

Sphn tch ny c dng nh gi v snh hng ca ba yu t trn cc

gi tr quan st G (i = 1, 2... r: yu t A; j = 1, 2... r: yu t B; k = 1, 2... r: yu t C)

M hnhKhi nghin cu nh hng ca 2 yu t, mi yu t c n mc, th ngi ta dng

m hnh vung latinh nn. V dnh m hnh vung latinh 44:

B C D AC D A BD A B CA B C D

M hnh vung latinh 3 yu tc trnh by nh sau:

Yu t C (T..k. v d: T...1 = Y111 + Y421 + Y334 + Y241)


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Bng ANOVA

Ngun sais

Bc tdo Tng sbnh phngBnh phng trung

bnhGi tr

thng k

Yu t A

(hng)

(r1)

Yu t B(ct)

(r1)

Yu t C (r1)

Sai s (r -1)(r -2)SSE = SST - (SSF + SSR +

SSC)

Tng cng (r21) ij

Trc nghim

Gi thit:

H0: 1 = 2= .= kCc gi tr trung bnh bng nhau

H1: i jC t nht hai gi tr trung bnh khc nhau

Gi tr thng k: v

Bin lun:

- Nu (chp nhn H0(yu t A))- Nu (chp nhn H0(yu t B))- Nu (chp nhn H0(yu t C))P DNG MS-EXCEL

Nhp dliu vo bng tnh

Thit lp mt s biu thc v tin hnh tnh ton:Tnh cc gi tr Titng theo hng t B n E


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- Chn B7 v nhp biu thc=SUM(B2:E2)- Chn C7 v nhp biu thc =SUM(B3:E3)- Chn D7 v nhp biu thc =SUM(B4:E4)- Chn E7 v nhp biu thc =SUM(B5:E5)

Tnh cc gi tr Tjtng theo ct t hng th n hng th

- Chn B8 v nhp biu thc =SUM(B2:B5)- Dng con tr ko k hiu t in t B8 n E8

Tnh cc gi tr Tk

- Chn B9 v nhp biu thc =SUM(B2,C5,D4,E3)- Chn C9 v nhp biu thc =SUM(B3,C2,D5,E4)- Chn D9 v nhp biu thc =SUM(B4,C3,D2,E5)- Chn E9 v nhp biu thc =SUM(B5,C4,D3,E2)

Tnh gi tr Ttng cc phn t trong bng

- Chn B10 v nhp biu thc=SUM(B2:E5)Tnh cc gi tr v

oCc gi tr v - Chn G7 v nhp biu thc =SUMSQ(B7:E7)- Dng con tr ko k hiu t in t G7 n G9oGi tr

- Chn G10 v nhp biu thc =POWER(B10,2)oGi tr

- Chn G11 v nhp biu thc =SUMSQ(B2:E5)Tnh cc gi tr SSSSCSSFSST v SSE

oCc gi tr SSSSC v SSFoGi tr SSR

- Chn I7 v nhp biu thc =G7/4-39601/POWER(4.2)- Dng con tr ko k hiu t in t I7 n I9oGi tr SST

- Chn I11 v nhp biu thc =G11-G10/POWER(4.2)oGi tr SSE

- Chn I10 v nhp biu thc =I11-SUM(I7:I9)Tnh cc gi tr SSCSF v SE


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oCc gi tr SSC v SF- Chn K7 v nhp biu thc=I7/(4-1)- Dng con tr ko k hiu t in t K7 n K9

oGi tr SE- Chn K10 v nhp biu thc =I10/((4-1)*(4-2))

oTnh cc gi tr F FC v F- Chn M7 v nhp biu thc =K7/K10- Chn M8 v nhp biu thc =K8/K10- Chn M9 v nhp biu thc =K9/K10

Ta c:

t qu v bin lun:

o FR=3.11 F0.05(3.) = 4. =bc b H0(nhit )o F =30.05 > F0.05(3.6) = 4.76 =bc b H0(cht xc tc)

Kt lun:Vy ch c nhit v cht xc tc nh hng n hiu sut.

Cu 2:(V d 4.2/216/Gio trnh XSTKGS-TS Nguyn nh Huy)

Ngi ta dng 3 mc nhit gm 105, 120, 135oC kt hp vi 3 khong thi

gian l 15, 30 v 0 pht thc hin mt phn ng tng hp. Cc hiu sut phn

ng(%) c trnh by trong bng sau:


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Thi gian(pht)X1

Nhit C)X2

Hiu sut %Y

15 105 1.8730 105 2.0260 105 3.2815 120 3.0530 120 4.0760 120 5.5415 135 5.0330 135 6.4560 135 7.26

Hy cho bit yu t nhit v thi gian hoc yu t thi gian c lin quan tuyn

tnh vi hiu sut ca phn ng tng hp? Nu c th iu kin nhit 115oC trong

vng 50 pht th hiu sut phn ng l bao nhiu?

Gii

DNG TON:

Hi quy tuyn tnh a tham s.

C S L THUYT:

Trong phng trnh hi quy tuyn tnh a tham s, bin s ph thuc Y c lin

quan n k bin s c lp Xi(i = 1, 2,..., k) thay v ch c mt nh trong hi quy tuyn

tnh n gin.

Phng trnh tng qut:

Bng ANOVA

Ngun sai s Bc tdoTng s bnh

phngBnh phng trung

bnhGi tr

thng k

Hi quy k SSR MSR = SSR/k Sai s Nk1 SSE MSE = SSE/(Nk1)

Tng cng N1 SST = SSR + SSE


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Gi tr thng k:oGi tr Rbnh phng:

Gi tr

( l kh tt)Gi trc hiu chnh

( s trnn m hoc khng xc nh nu hoc N nh)

o lch chun:

(S 0.30 l kh tt)

Trc nghim thng k:oTrong trc nghim t:

: Cc h s hi quy khng c ngha

:

C t nht mt s h s hi quy c ngha

Bc t do ca gi tr t: || ;

oTrong trc nghim F:: phng trnh hi quy khng thch hp: phng trnh hi quy thch hp vi t nht vi

Bc t do ca gi tr F: ; P DNG MS-EXCEL

Nhp dliu vo bng tnh

D liu nht thit phi nhp theo ct


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S dng chng trnh egression trong thData Data Analysis

Chn OKhp thoi Regression xut hin

Phng trnh hi quy = f(X1)Kim nh gi thit Ho: thi gian khng lin quan tuyn tnh vi hiu sut ca

phn ng tng hp


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Trong hp thoi Regression,ln lt chn cc chi tit:

- Phm vi ca bin s Y (Input Y range)- Phm vi ca bin s X (Input X range)-Nhn d liu(Labels)- Mc tin cy(Confidence level)- Ta u ra(Output range)- ng hi quy(line Fit Plots),

Ta c kt qu:


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Phng trnh hi quy

(R2= 0.21; S=1.81) (1)

to = 2.129 = 0.05)

chp nhn gi thit Ho

t1= 1.380 = 0.05)

chp nhn gi thit Ho

F = 1.905 = 0.05)

chp nhn gi thit Ho

Vy c 2 h s 2.73(B0) v 0.04(B1) ca phng trnh hi quy (I)u khng c

ngha thng k. Ni cch khc,phng trnh hi quy ny khng thch hp.

Kt lun:Vy yu t thi gian khng lin quan tuyn tnh vi hiu sut ca phn ng

tng hp.

Phng trnh hi quy = f(X2)Kim nh gi thit H

o: nhit khng lin quan tuyn tnh vi hiu sut ca

phn ng tng hp.


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Ta c kt qu:


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Phng trnh hi quy (R2 = 0.76; S = 0.99) (II)to =3.418 > t0.05 = 2.365 (Pv

2 = 0.0112 t0.05 = 2.365 (Pv = 0.0021F0.05(1,7)

= 5.59 (Fs =0.0021


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13/30



Phng trnh hi quy

(R2 = 0.98; S = 0.33) (III)to= 11.528 > t0.05 = 2.447 (Pv= 2.56E-05 t0.05 = 2.447 (Pv=0.00027 t0.05 = 2.447 (Pv = 7.234E-06F0.05(2,6)= 5.140 ( hay Fs =1.112E-05


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Vi B0, B1, B2 l h sphng trnh hi quy (III)

Kt quthu c nh sau:

BI 2:

Bnh au mt ht c chia lm 4 thi k T1, T2, T3 v T4. Kt qu kim tra mt ht 3 tnh

A, B, C c cho trong bng sau y:

aphng

Mc au mt htT1 T2 T3 T4

A 47 189 807 1768B 53 746 1387 946C 16 228 438 115

Hy nhn nh xem tnh hnh au mt ht (c cu phn b cc mc T1, T2, T3, T4)

3 tnh trn c ging nhau hay khng? Mc ngha 1%.

Gii:

DNG TON:

So snh t s.

C S L THUYT:

Gi thit

H0 : P1 = P1,0, P2 = P2,0,., Pk,0Cc cp Pi v Pi,0 ging nhau.

H1 : C t nht mt cp Pi v Pi,0 khc nhau.Gi tr thng k

[ ]

Oi : cc tn s thc nghim (observed frequency).

Ei: cc tn s l thuyt (expected frequency).

Bin lunNu bc b gi thit Ho (DF = k-1)


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Trong MS-Excel c hm CHITEST c th tnh:

Gi tr2 theo biu thc:

( )

Oi j: tn s thc nghim ca thuc hng th i ct j.

Ei j : tn s l thuyt ca thuc hng th i ct j; r l s hng; c l s ct.

Xc sut P(X >2)vi bc t do DF = (r-1)(c-1); trong r l s hng; c l s ct

trong bng ngu nhin (contingency table).

Nu P(X >) chp nhn gi thit Hov ngc li.P DNG MS-EXCEL

Nhp dliu vo bng tnh

Sp xp d liu theo bng trc nghim hai mu c lp.

Thit lp mt s biu thc v tin hnh tnh ton:Tnh cc tng s:

oTng hng (Row totals): Chn F3 v nhp vo biu thc =SUM(B3:E3)Dng con tr ko nt tin t F3n F5

oTng ct (Column totals): Chn B6 v nhp vo biu thc=SUM(B3:B5)Dng con tr ko nt tin t B6n E6

oTngcng (Grand total): Chn F6 v nhp biu thc=SUM(F3:F5) hoc=SUM(B6:E6)

Tnh cc tn s l thuyt:

Tn s l thuyt = (tng hng tng ct) / tng cngoCc tn s ti tnh A:

- Mc au mt ht T1: chn B9 v nhp vo biu thc=F3*B6/F6- Mc au mt ht T2: chn C9 v nhp vo biu thc=F3*C6/F6-Mc au mt ht T3: chn D9 v nhp vo biu thc=F3*D6/F6

- Mc au mt ht T4:chn E9 v nhp vo biu thc=F3*E6/F6


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oCc tn s ti tnh B:- Mc au mt ht T1:chn B10 v nhp vo biu thc=F4*B6/F6- Mc au mt ht T2: chn C10 v nhp vo biu thc=F4*C6/F6- Mc au mt ht T3: chn D10 v nhp vo biu thc =F4*D6/F6- Mc au mt ht T4: chn E10 v nhp vo biu thc =F4*E6/F6

oCc tn s ti tnh C:- Mc au mt ht T1: chn B11 v nhp vo biu thc =F5*B6/F6- Mc au mt ht T2: chn C11 v nhp vo biu thc =F5*C6/F6- Mc au mt ht T3:chn D11 v nhp vo biu thc =F5*D6/F6- Mc au mt ht T4: chn E11 v nhp vo biu thc =F5*E6/F6

Tnh xc sut P(X >) :Chn B13 v nhp vo biu thc =CHITEST(B3:E5,B9:E11)

Ta c:

Hoc chn FormulasMore FunctionsStatistical CHITEST


17/30



Xut hin hp thoi Function Agruments

Nhp cc gi tr tn s quan st vo mc Actual_range Nhp cc gi tr tn s l thuyt vo mc Expected_range Chn OK

Ta c P = 6.0949E-215 0.01 nn bc b gi thuyt Kt lun:Nh vy tnh hnh au mt ht 3 tnh trn khng ging nhau.

BI 3:

Bng sau y cho s liu ngi cht v ung th 3 nc M, Nht v Anh. Ngi cht

c phn loi theo c quan b ung th.

Ch ung thNc

M Nht AnhRut

NgcD dyB phn khc

1115341

532230

57315

a) Hy tnh tn s l thuyt cabng s liu trn.

b) C th p dng tiu chun 2c khng?

c) Vi mc ngha = 1% hy so snh phn b t l cht vung th ca ba

nc ni trn.


18/30



Gii:

DNG TON:

So snh t s.

C S L THUYT:

Gi thit

H0 : P1 = P1,0, P2 = P2,0,., Pk,0Cc cp Pi v Pi,0 ging nhau.

H1 : C t nht mt cp Pi v Pi,0 khc nhau.

Gi tr thng k

[ ]

Oi : cc tn s thc nghim (observed frequency).

Ei : cc tn s l thuyt (expected frequency).

Bin lun

Nu bc b gi thit Ho (DF = k-1)Trong MS-Excel c hm CHITEST c th tnh:

Gi tr2 theo biu thc:

( ) Oi j : tn s thc nghim ca thuc hng th i ct j.

Ei j : tn s l thuyt ca thuc hng th i ct j; r l s hng; c l s ct.

Xc sut P(X >2)vi bc t do DF = (r-1)(c-1); trong r l s hng; c l s ct

trong bng ngu nhin (contingency table).

Nu P(X >

)

chp nhn gi thit Hov ngc li.

P DNG MS-EXCEL

Nhp dliu vo bng tnh

Sp xp d liu theo bng trc nghim hai mu c lp.


19/30



Thit lp mt s biu thc v tin hnh tnh ton:

Tnh cc tng s:

oTng hng (Row totals): Chn E3 v nhp vo biu thc =SUM(B3:D3)Dng con tr ko nt tin t E3n E6

oTng ct (Column totals): Chn B7 v nhp vo biu thc =SUM(B3:B6)Dng con tr ko nt tin t B7n D7

oTngcng (Grand total): Chn E7 v nhp biu thc =SUM(B7:D7) hoc=SUM(E3:E6)

Tnh cc tn s l thuyt:

Tn s l thuyt = (tng hng tng ct) / tng cngoCc tn sung th rut:

- Ti M: chn B10 v nhp vo biu thc =E3*B7/E7- Ti Nht: chn C10 v nhp vo biu thc =E3*C7/E7- Ti Anh: chn D10 v nhp vo biu thc =E3*D7/E7

oCc tn sung th ngc:- Ti M: chn B11 v nhp vo biu thc =E4*B7/E7- Ti Nht: chn C11 v nhp vo biu thc =E4*C7/E7- Ti Anh: chn D11 v nhp vo biu thc =E4*D7/E7

oCc tn sung th d dy:- Ti M: chn B12 v nhp vo biu thc =E5*B7/E7- Ti Nht: chn C12 v nhp vo biu thc =E5*C7/E7- Ti Anh: chn D12 v nhp vo biu thc =E5*D7/E7

oCc tn sung th b phn khc:- Ti M: chn B13 v nhp vo biu thc =E6*B7/E7- Ti Nht: chn C13 v nhp vo biu thc =E6*C7/E7- Ti Anh: chn D13 v nhp vo biu thc =E6*D7/E7

- V tn s l thuyt ca rut, ngc Anh 5 nn khng th p dng tiu chun

2ta phi ghp rut v ngc.


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Nhp li dliu vo bng tnh

C th p dng tiu chun 2v cc tn s l thuyt Tnh xc sut P(X >) :

Chn B15 v nhp vo biu thc =CHITEST(B3:D6;B10:D13)

Hoc chn FormulasMore FunctionsStatistical CHITEST


21/30



Xut hin hp thoi Function Agruments

Nhp cc gi tr tn s quan st vo mc Actual_range Nhp cc gi tr tn s l thuyt vo mc Expected_range Chn OK

Ta c P = 7,5363E-06 0.01 nn bc b gi thuyt Kt lun:Nh vy tnh hnh ung th cc nc l khc nhau.

BI 4:

Theo di doanh thu ca 4 ca hng thuc mt Cng ty (triu /thng) ngi ta c s

liu nh sau:

Thngkinh doanh

Ca hng1 2 3 4

123456

12,312,611,615,218,617,1

14,212,411,511,6

15,617,118,212,511,8

17,215,812,2

Hy so snh doanh thu trung bnh/thng ca cc ca hng thuc Cng ty ni trn. Mc

ngha = 5%.

Gii:

DNG TON:

Phn tch phng sai mt yu t.

C S L THUYT: Khi nim thng k


22/30



Php phn tch phng sai c dng trong cc trc nghim so snh cc gi tr

trung bnh ca hai hay nhiu mu c ly t cc phn s.

y c thc xem nhphn mrng cc trc nghim t hay z (so snh hai gi tr

trung bnh).

Mc ch ca sphn tch phng sai mt yu tl nh gi snh hng ca

mt yu t (nhn to hay tnhin) no trn cc gi tr quan st, Yi(i=0,1,2,,k).

M hnh

Yu t th nghim

1 2 .. K

Y11 Y21 .. Yk1

Y12 Y22 .. Yk2.. .. .. ..Y1N Y2N .. YkN

Tng cng

trung bnh

T1

1

___

Y

T2

2

___

Y ..

..

Tk

kY___

TBng ANOVA

Ngun sai

s

Bc sai

s

Tng s bnh

phng

Bnh phng trung

bnh

Gi tr thng

k

Yu t

Sai s

k-1

N-k

SSF=N

T

N

Tk

i

i

2

1

2

SSE=SST-SSF

MSF=1k

SSF

MSE=kN

SSE

F=

MSE

MSF

Tng cng N-1 SST=N

TY

k

i

N

j

n

2

1 1

2

Trc nghim

Gi thit:

H0: k .....21 Cc gi tr trung bnh bng nhau

H1: ji t nht c hai gi trtrung bnh khc nhau

Gi tr thng k: F=MSE

MSF

Bin lun: Nu F < F(k-1;N-k) => chp nhn gi thit H0P DNG MS-EXCEL


23/30



Gi thitH0: 1 = 2 = 3= 4; tc doanh thu trung bnh/thng ca cc ca

hng bng nhau

Nhp dliu vo bng tnh

p dng Anova: Single Factor

Chn DataData Analysis

Chn chng trnh Anova: Single Factor trong hp thoi Data Analysis ri nhn nt

OK

Trong hp thoi Anova: Single Factor ln lt n nh

Phm vi u vo (Input range)Cch sp xp theo hng hay ct (Group by)Nhn d liu (Labels in fisrt row/column)Phm vi u ra (Output range)


24/30



Bng Anova:

Anova: Single

Factor

SUMMARY

Groups Count Sum Average Variance1 6 87.4 14.56667 8.178666667

2 4 49.7 12.425 1.5625

3 5 75.2 15.04 7.873

4 3 45.2 15.06667 6.653333333

ANOVA

Source of

Variation SS df MS F P-value F crit

Between Groups 18.98994 3 6.329981 0.980529221 0.429943 3.343889

Within Groups 90.3795 14 6.455679

Total 109.3694 17


25/30



Kt qu v bin lun

T gi tr trong bng Anova:

F= 0.980529221< F= 3.343889

=> Chp nhn H0

= Lng doanh thu trung bnh/thng ca ccca hng thuc Cng ty l nh nhau.

BI 5:

Vi mc ngha 1%, Hy phn tch tnh hnh kinh doanh mt s ngnh ngh 4 qun

ni thnh trn c s s liu v doanh thu ca mt s ca hng nh sau:

Ngnh ngh

kinh doanh

hu vc kinh doanh

Q1 Q2 Q3 Q4in lnh

Vt liu

xy dng

Dch v

tin hc

2.5:2.7:2.0:3.0

0.6:10.4

1.2:1.0:9.8:1.8

3.1:3.5:2.7

15.0

2.0:2.2:1.8

2.0:2.4

9.5:9.3:9.1

1.2:1.3:1.2

5.0:5.4

19.5:17.5

5.0:4.8:5.2

Gii:DNG TON:

Phn tch phng sai hai yu t (c lp) .

C S L THUYT:

Khi nim thng k

Bi ton phn tch phng sai 2 yu t c lp tng t nh bi ton phn tch

phng sai 2 yu t khng lp, ch khc mi mc (Ai, Bj) u c s lp li r ln th

nghim v ta cn kho st thm stng tc (interaction term) F1 gia 2 nhn t A vB.

Mu iu tra:


26/30



X l mu:


27/30




28/30



P DNG MS-EXCEL

Gi thuyt:

H0(yu t ngnh ngh): tnh hnh kinh doanh mt s ngnh ngh bn qun l nh

nhau.

Ho(yu t qun):tnh hnh kinh doanh 4 qun l nh nhau

Nhp dliu vo bng tnh

p dng: Anova: two-factor with replication.


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Hp thoi: Anova: two-factor with replication. Hin ra.


30/30


Kt lun:

FR< F0.01=5.25 => chp nhn gi thuyt H0 (Tnh hnh kinh doanh gia cc ngnh ngh

l nh nhau).

FC = 0.8189 < F0.01 = 4.38 => chp nhn gi thuyt H0 (Tnh hnh kinh doanh gia cc

qun l nh nhau)

FI = 0.6498 < F 0.01 = 3.35 => chp nhn gi thuyt H0 (Tnh hnh kinh doanh gia cc

qun v ngnh nghnh nhau)

Vy tnh hnh kinh doanh l nh nhau khng nhng gia cc ngnh ngh m cn

gia cc qun. Ngoi ra, khng c stng tc gia hai yu t ngnh ngh kinh doanh

v a im kinh doanh (qun)

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