20140905 Probability Sam

7/25/2019 20140905 Probability Sam

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BIODATA SINGKATBIODATA SINGKAT NAMA : Prof. DR. SAMSUBAR SALEH. M.Soc.ScNAMA : Prof. DR. SAMSUBAR SALEH. M.Soc.Sc PEKERJAAN : DOSEN FEB-UGMPEKERJAAN : DOSEN FEB-UGM JABATAN : GURU BESAR ILMU EKONOMI IV/cJABATAN : GURU BESAR ILMU EKONOMI IV/c ALAMAT : JL WELING II / ! A. DEPOK-SLEMANALAMAT : JL WELING II / ! A. DEPOK-SLEMAN BIDANG MINAT : EKONOMI-PUBLIKBIDANG MINAT : EKONOMI-PUBLIK STATISTIKA TERAPANSTATISTIKA TERAPAN

TEORI EKONOMI MAKRO/MIKROTEORI EKONOMI MAKRO/MIKROPENGALAMAN KERJA : DOSEN FEB-UGMPENGALAMAN KERJA : DOSEN FEB-UGM : ASSISTEN WADEK III " SEK-JURUSAN IE.: ASSISTEN WADEK III " SEK-JURUSAN IE. : PENGELOLA S#/S FEB-UGM: PENGELOLA S#/S FEB-UGM : SUPERVISOR BSNP DIKNAS: SUPERVISOR BSNP DIKNAS

: PENGELOLA PENELITIAN EKONOMI: PENGELOLA PENELITIAN EKONOMI : KONSULTAN PEREN$/PEMB DI%: KONSULTAN PEREN$/PEMB DI% : KONSULTAN " FASILITATOR KEU-DA: KONSULTAN " FASILITATOR KEU-DAHP: &'((#)##*.HP: &'((#)##*.E+, :,+01,r23,4oo.co+E+, :,+01,r23,4oo.co+


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T567-Boo8T567-Boo8

(. L9 " M,rc4,; S7,77c for B095(. L9 " M,rc4,; S7,77c for B095 #. Wo99,co77 : S7,77c#. Wo99,co77 : S7,77c

. S,+01,r S,54: S7,778 I9087f. S,+01,r S,54: S7,778 I9087f


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PROBABILITYPROBABILITYPROBABILITYPROBABILITYIS A NUMERI$AL MEASURE OF THEIS A NUMERI$AL MEASURE OF THE

LIKELIHOOD OF AN EVENT OR MORE O$$URRING orLIKELIHOOD OF AN EVENT OR MORE O$$URRING or$HAN$E AN EVENT OR MORE WILL O$$UR AS A RESULT$HAN$E AN EVENT OR MORE WILL O$$UR AS A RESULTOF AN E


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EXPERIMENT, OUTCOMES AND EVENTEXPERIMENT, OUTCOMES AND EVENT

EA$H E


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THE MULTIPLICATION RULE OF PROBABILITYTHE MULTIPLICATION RULE OF PROBABILITY

(.(. INDEPENDENT EVENTS: TWO EVENTS AREINDEPENDENT EVENTS: TWO EVENTS AREINDEPENDENT WHEN THE O$$URREN$E OF ONEINDEPENDENT WHEN THE O$$URREN$E OF ONEEVENT HAS NO EFFE$T ON THE PROBABIEVENT HAS NO EFFE$T ON THE PROBABILLIT% OFIT% OFO$$URREN$E OF THE OTHER EVENT.O$$URREN$E OF THE OTHER EVENT.

P @ A ,9 B ? P @ A . P @ B P @ A ,9 B ? P @ A . P @ B

#. DEPENDENT EVENT: TWO EVENTS ARE DEPENDENT#. DEPENDENT EVENT: TWO EVENTS ARE DEPENDENT

WHEN THE O$$URREN$E OF ONE EVENT AFFE$T THEWHEN THE O$$URREN$E OF ONE EVENT AFFE$T THE PROBABILIT% OF O$$URREN$E OTHER EVENT.PROBABILIT% OF O$$URREN$E OTHER EVENT.

P @ A ,9 B ? P @ A . P @ B/A P @ A ,9 B ? P @ A . P @ B/A


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ExampleExample

A BO< $ONTAINS OF (& RED BALLS= > WHITEA BO< $ONTAINS OF (& RED BALLS= > WHITEBALLS AND * BLUE BALLS. ONE BALL ISBALLS AND * BLUE BALLS. ONE BALL ISSELE$TED AT RANDOM TIMES. WHAT ISSELE$TED AT RANDOM TIMES. WHAT IS

THE PROBABILIT% of OBTAINING:THE PROBABILIT% of OBTAINING:,.,. A 1, ,r5 475 @ 74 r5C,c5+597 .A 1, ,r5 475 @ 74 r5C,c5+597 .1.1. A 1, ,r5 475 @ 74o07 r5C,c5+597 .A 1, ,r5 475 @ 74o07 r5C,c5+597 .c.c. T45 (7 55c7o9 r5= 745 #9 55c7o9 r5 ,9 745 rT45 (7 55c7o9 r5= 745 #9 55c7o9 r5 ,9 745 r

55c7o9 105 @ 74o07 r5C,c5+597 .55c7o9 105 @ 74o07 r5C,c5+597 ... T45r5 ,r5 # r5 1, ,9 (T45r5 ,r5 # r5 1, ,9 ( 1051051, @ 74o07 r5C,c5+597 1, @ 74o07 r5C,c5+597 5.5. T45r5 ,r5 ( r5= ( 475 ,9 ( 105 1, @ W74o07 R.T45r5 ,r5 ( r5= ( 475 ,9 ( 105 1, @ W74o07 R.


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THE RULES OF PROBABILITYTHE RULES OF PROBABILITY

THE ADDITION RULE OF PROBABILIT%:THE ADDITION RULE OF PROBABILIT%:

(.(. FOR MUTUALLY EXCLUSIVE EVENTS.FOR MUTUALLY EXCLUSIVE EVENTS.

P @ A or B ? P @ A P @ B P @ A or B ? P @ A P @ B

EVENTS A " B $ANT O$$UR SIMULTANEOUSL%EVENTS A " B $ANT O$$UR SIMULTANEOUSL%

OR AT THE SAME TIME.OR AT THE SAME TIME.

#.#. FOR NON-MUTUALLY EXCLUSIVE EVENTS:FOR NON-MUTUALLY EXCLUSIVE EVENTS:

P @ A or B ? P @ A P @ B P @ A ,9 B P @ A or B ? P @ A P @ B P @ A ,9 B A ,9 B $AN O$$UR SIMULTANEOUSL%.A ,9 B $AN O$$UR SIMULTANEOUSL%.


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CONDITIONALCONDITIONALPROBABILITYPROBABILITY

THE PROBABILIT% OF A PARTI$ULARTHE PROBABILIT% OF A PARTI$ULAREVENT O$$URING= GIVEN THATEVENT O$$URING= GIVEN THATANOTHER EVENT HAS ALREAD%ANOTHER EVENT HAS ALREAD%O$$URRED.O$$URRED.

IF= P @ A ,9 B ? P @ A . P @ B/A = THUS;IF= P @ A ,9 B ? P @ A . P @ B/A = THUS;

P @ A ,9 B P @ A ,9 B P @ B/A ? -------------------------P @ B/A ? -------------------------

P @ A P @ A


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EXAMPLEEXAMPLE

S$ORES :S$ORES : A B $ FA B $ F$LASSES$LASSES

. P @ /F *. P @ or A ). P @ $/< >. P @ /F


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E6,+C5E6,+C5 I' La(& A, )*e+e a+e 10 '-). A/e+ /mp)e+, 5 '-). Cmpa/)I' La(& A, )*e+e a+e 10 '-). A/e+ /mp)e+, 5 '-). Cmpa/)

a' 15 '-). T.*-(a2 I' la(& B, )*e+e a+e 15 '-). A/e+a' 15 '-). T.*-(a2 I' la(& B, )*e+e a+e 15 '-). A/e+/mp)e+., 10 '-) Cmpa/) a' 10 '-). T.*-(a2 I' la(& C,/mp)e+., 10 '-) Cmpa/) a' 10 '-). T.*-(a2 I' la(& C,)*e+e a+e 10 '-). A/e+, 10 '-). Cmpa/) a' 10 '-).)*e+e a+e 10 '-). A/e+, 10 '-). Cmpa/) a' 10 '-).

T.*-(a2T.*-(a2 A2 I3 ea/* la( -. .ele/)e 'e /mp)e+ +a'ml4, *a) -. )*eA2 I3 ea/* la( -. .ele/)e 'e /mp)e+ +a'ml4, *a) -. )*e

p+(a(-l-)4 )*a) all 3 )*e /mp)e+. a+e T.*-(a2p+(a(-l-)4 )*a) all 3 )*e /mp)e+. a+e T.*-(a2 B2 I3 'e /mp)e+ -. .ele/)e a) +a'm 3+m 'e la(, *a) -.B2 I3 'e /mp)e+ -. .ele/)e a) +a'm 3+m 'e la(, *a) -.

)*e p+(a(-l-)4 )*a) )*e /mp)e+ -. A/e+ + Cmpa/)2)*e p+(a(-l-)4 )*a) )*e /mp)e+ -. A/e+ + Cmpa/)2


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BAYES6S RULE FOR CONDITIONAL PROBABILITYBAYES6S RULE FOR CONDITIONAL PROBABILITY

P @ A P @ B/A P @ A P @ B/A P @ A/B ? ----------------------------------------------------------P @ A/B ? ---------------------------------------------------------- P @ A( P @ B/A( ------- P @ A9 P @ B/A9 P @ A( P @ B/A( ------- P @ A9 P @ B/A9 E


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Example&!Example&!

T45 90+15r of 70597 fro+ c, A ? )= c, BT45 90+15r of 70597 fro+ c, A ? )= c, B? &= c, $ ? *& ,9 c, D ? #). B,5 o9 745? &= c, $ ? *& ,9 c, D ? #). B,5 o9 74556,+9,7o9 r5cor= 7 , fo09 74,7 (& of56,+9,7o9 r5cor= 7 , fo09 74,7 (& of

70597 fro+ c, A , f,= c, B ? )= c,70597 fro+ c, A , f,= c, B ? )= c,$ ? () ,9 c, D ? #& . If o95 70597 ,$ ? () ,9 c, D ? #& . If o95 70597 ,55c75 ,7 r,9o+ , 9c,75 74,7 45 555c75 ,7 r,9o+ , 9c,75 74,7 45 59 745 56,+. W4,7 745 Cro1,173 74,7 45 9 745 56,+. W4,7 745 Cro1,173 74,7 45

fro+ c, B or D.fro+ c, B or D.


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M,745+,7c, E6C5c7,7o9M,745+,7c, E6C5c7,7o9

F99 745 56C5c75 ,05 of 745 M5,9= V,r,9c5 ,9F99 745 56C5c75 ,05 of 745 M5,9= V,r,9c5 ,9S7,9,r D5,7o9 of , Cro1,173 7r107o9:S7,9,r D5,7o9 of , Cro1,173 7r107o9:

M5,9 ?M5,9 ?


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E6,+C5E6,+C5

A 3am-l4 *a. 3-8e /*-l+e'2 Plea.e /al/la)e )*eA 3am-l4 *a. 3-8e /*-l+e'2 Plea.e /al/la)e )*eexpe/)e 8ale a' .)a'a+ e8-a)-' 3 *a8-'9 maleexpe/)e 8ale a' .)a'a+ e8-a)-' 3 *a8-'9 male/*-l+e'2/*-l+e'2

S)ep1 & 3-' ) )*e 8ale 3 X- : male /*-l+e' ;2S)ep1 & 3-' ) )*e 8ale 3 X- : male /*-l+e' ;2 S)ep !& 3-' ) )*e p+(a(-l-)4 3 *a8-'9 X-2S)ep !& 3-' ) )*e p+(a(-l-)4 3 *a8-'9 X-2 X- &


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E6,+C5E6,+C5 T*e =a')-)4 3 X ema'e p+(a(-l-)4T*e =a')-)4 3 X ema'e p+(a(-l-)4

!00 '-). 0215!00 '-). 0215 !!5 02!0!!5 02!0 !50 02"0!50 02"0

!$5 02!5!$5 02!5 "00 0210"00 0210a2 >*a) -. )*e mea' 3 =a')-)4 3 X ema'e2a2 >*a) -. )*e mea' 3 =a')-)4 3 X ema'e2

(2 >*a) -. )*e 8a+-a'/e 3 )*e -.)+-()-'*a) -. )*e 8a+-a'/e 3 )*e -.)+-()-'*e' )*e p+-/e 3 X ? @ 10 a' AC ? @ /2 >*e' )*e p+-/e 3 X ? @ 10 a' AC ? @ >*a) -. )*e expe/)e 8ale 3 )*e p+3-)*a) -. )*e expe/)e 8ale 3 )*e p+3-)*a) -. )*e -33e+e'/e -' mea'-'9 (e)ee' )*e3-+.) a' )*e .e/' )e+m.23-+.) a' )*e .e/' )e+m.2


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STANDARD NORMAL VALUESTANDARD NORMAL VALUE@ @

XX-- GG--? ?

GG-- MEASURESMEASURESTHE DISTANCE OF ANYTHE DISTANCE OF ANYPARTICULAR VALUE OF X FROM THEPARTICULAR VALUE OF X FROM THE ,,MEASURED IN UNITS OF THE STANDARDMEASURED IN UNITS OF THE STANDARDDEVIATION2DEVIATION2

THE SIN OF G MIHT BE POSITIVE, NEATIVETHE SIN OF G MIHT BE POSITIVE, NEATIVEOR GERO2 IT DEPENDS ON THE DIFFERENCEOR GERO2 IT DEPENDS ON THE DIFFERENCEBET>EEN XBET>EEN X--VALUE AND ITS MEAN :VALUE AND ITS MEAN : ;2;2


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Example& : GExample& : G--8ale &appe'-x D8ale &appe'-x D,,p&$!0;p&$!0;

T45 cor5 of #)& 70597 9 +,745+,7c c, foo 745T45 cor5 of #)& 70597 9 +,745+,7c c, foo 7459or+, 7r107o9= 74 , +5,9 of >! ,9 7,9,r9or+, 7r107o9= 74 , +5,9 of >! ,9 7,9,r5,7o9 of (&. W4,7 745 Cro1,173 or ,r5, 095r 745,7o9 of (&. W4,7 745 Cro1,173 or ,r5, 095r 749or+, c0r5 for 745 cor5 :9or+, c0r5 for 745 cor5 :

,.,. B57559 >& ,9 >).B57559 >& ,9 >).

1.1. '&'&

c.c. B57559 >* ,9 '&.B57559 >* ,9 '&.

.. If 745 +9+0+ C,9 r,5 )). 4o +,93 70597 f,If 745 +9+0+ C,9 r,5 )). 4o +,93 70597 f,

9 74 56,+.9 74 56,+.

5.5. W4,7 745 +9+0+ cor5 for ) 745 157.W4,7 745 +9+0+ cor5 for ) 745 157.

f.f. W4,7 745 +,6+0+ cor5 for .) ,1o5 745 ,5r,5.W4,7 745 +,6+0+ cor5 for .) ,1o5 745 ,5r,5.


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N+mal D-.)+-()-'N+mal D-.)+-()-'

A9 55c7rc, fr+A9 55c7rc, fr++,90f,c70r5 47 101 74,7 4,5 ,+,90f,c70r5 47 101 74,7 4,5 ,5974 of f5 74,7 9or+,3 7r1075 74 +5,9 '&&5974 of f5 74,7 9or+,3 7r1075 74 +5,9 '&&4o0r ,9 ,r,9c5 of (>&& 4o0r. F9 745 Cro1,173:4o0r ,9 ,r,9c5 of (>&& 4o0r. F9 745 Cro1,173:

,. T4,7 , 101 10r9 157559 ' ,9 '* 4o0r.,. T4,7 , 101 10r9 157559 ' ,9 '* 4o0r.

1. T4,7 , 101 10r91. T4,7 , 101 10r9 ')& 4o0r or ) 4o0r. ')& 4o0r or ) 4o0r.

c. T4,7 , 101 10r9 157559 #& ,9 '& 4o0r.c. T4,7 , 101 10r9 157559 #& ,9 '& 4o0r.

. T45 +9+0+ 5974 of f5 for (#.) 745 o957.. T45 +9+0+ 5974 of f5 for (#.) 745 o957.

5. T45 +9+0+ 5974 of f5 for ## 15o 745 ,5r,5.5. T45 +9+0+ 5974 of f5 for ## 15o 745 ,5r,5.


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MID-E


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MID EHEN U FIND ANY DIFFICULTIES PLEASE>HEN U FIND ANY DIFFICULTIES PLEASEDISCUSS >ITH ME OR CONTACT TODISCUSS >ITH ME OR CONTACT TO011!5"!!%2011!5"!!%2


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T*e N+mal app+x-ma)-' ) )*e B-'m-alT*e N+mal app+x-ma)-' ) )*e B-'m-al

B9o+, 7r107o9 5ff5c75 f 745 90+15r ofB9o+, 7r107o9 5ff5c75 f 745 90+15r of7r, r5,753 +,. B07= 595r,79 , 19o+,7r, r5,753 +,. B07= 595r,79 , 19o+,7r107o9 for , ,r5 90+15r of 7r, o0 157r107o9 for , ,r5 90+15r of 7r, o0 155r3 7+5 co90+9. A +or5 5ffc597 ,CCro,c4 7o5r3 7+5 co90+9. A +or5 5ffc597 ,CCro,c4 7o

,CC3 745 9or+, ,CCro6+,7o9 7o 745 B9o+,:,CC3 745 9or+, ,CCro6+,7o9 7o 745 B9o+,:T45 ,CCro,c4 575r+95 , foo:T45 ,CCro,c4 575r+95 , foo:

? 9? 9 QQ


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ExampleExample

If (& of , 1095 565c075 f o07 , 59If (& of , 1095 565c075 f o07 , 59+,r8579 0r53 057o99,r5= 4,7 745+,r8579 0r53 057o99,r5= 4,7 745

Cro1,173 of 5779:Cro1,173 of 5779:,.,. A7 5,7 () 057o99,r5A7 5,7 () 057o99,r5 15 1,c8 15 1,c8o07 of #&&o07 of #&&

7r1075 7o 565c0757r1075 7o 565c075

1.1. W4,7 745 Cro1,173 74,7 157559 # ,9 W4,7 745 Cro1,173 74,7 157559 # ,9 &&057o99,r5 15 f5 o07057o99,r5 15 f5 o07

c.c. W4,7 745 Cro1,173 74,7 ( 057o99,r5 orW4,7 745 Cro1,173 74,7 ( 057o99,r5 or5 15 f5 o07.5 15 f5 o07.

Dont forget to !!"# t$e %orre%t&on f%tor'Dont forget to !!"# t$e %orre%t&on f%tor'


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E67r,-Bo90E67r,-Bo90

A +,90f,c70r5 Cro0c5 (&.&&& 097 of Cro0c7A +,90f,c70r5 Cro0c5 (&.&&& 097 of Cro0c7,3. O9 745 1, of fr50597 9C5c7o9 7 ,3. O9 745 1, of fr50597 9C5c7o9 7 co5r5= )&& 097 of Cro0c7 c,f5 ,co5r5= )&& 097 of Cro0c7 c,f5 ,5f5c75. W4,7 745 Cro1,173 74,7:5f5c75. W4,7 745 Cro1,173 74,7:

,.,. Mor5 74,9 )#) 097 of Cro0c7 5f5c75.Mor5 74,9 )#) 097 of Cro0c7 5f5c75.

1.1. A7 5,7 !*)& 097 of Cro0c7 oo.A7 5,7 !*)& 097 of Cro0c7 oo.

c.c. L5 74,9 *) 097 of Cro0c7 5f5c75.L5 74,9 *) 097 of Cro0c7 5f5c75... T45 90+15r of oo Cro0c7 157559 !*)& 097T45 90+15r of oo Cro0c7 157559 !*)& 097

,9 !))& 097.,9 !))& 097.


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T45 ,7 0 15for5 + 56,+T45 ,7 0 15for5 + 56,+

(. B9o+, 7r107o9(. B9o+, 7r107o9 #. Nor+, 7r107o9#. Nor+, 7r107o9

. Fro+ B9o+, 7o Nor+,.. Fro+ B9o+, 7o Nor+,.

T45 0 15 59 o9 T05,3 9567T45 0 15 59 o9 T05,3 9567

558. @ o97 for57 7o 1r9 3o0r c,c0,7or558. @ o97 for57 7o 1r9 3o0r c,c0,7or,9 7,77c 7,15.,9 7,77c 7,15.


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SAMPLIN METHODS ESTIMATIONSAMPLIN METHODS ESTIMATION

MODELSMODELS


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S,+C9 M574oS,+C9 M574o

REASONS TO SAMPLEREASONS TO SAMPLE(. TO OBSERVE THE WHOLE POPULATION WO(. TO OBSERVE THE WHOLE POPULATION WOUULD BELD BETIME $ONSUMING AND VER% E


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SAMPLIN METHODSSAMPLIN METHODS

(. SIMPLE RANDOM SAMPLE: A SAMPLE SELE$TED SO THAT(. SIMPLE RANDOM SAMPLE: A SAMPLE SELE$TED SO THATEA$H ITEM IN THE POPULATION HAS THE SAMEEA$H ITEM IN THE POPULATION HAS THE SAMEPROBABILIT% OF BEING IN$LUDED.PROBABILIT% OF BEING IN$LUDED.

#. S%STEMATI$ RANDOM SAMPLE: A RANDOM STARTING#. S%STEMATI$ RANDOM SAMPLE: A RANDOM STARTINGPOINT 8 IS SELE$TEPOINT 8 IS SELE$TEDD= AND THEN EVER%= AND THEN EVER% (t$(t$ MEMBER OFMEMBER OF

THE POPULATION IS SELE$TED.THE POPULATION IS SELE$TED. . STRATIFIED RANDOM SAMPLE : A POPULATION IS. STRATIFIED RANDOM SAMPLE : A POPULATION IS

DIVIDED INTO SUB-GROUPS= $ALLED STRATA= AND ADIVIDED INTO SUB-GROUPS= $ALLED STRATA= AND ASAMPLE IS RANDOML% SELE$TED FROMSAMPLE IS RANDOML% SELE$TED FROMEA$H STRATUM.EA$H STRATUM.

*.$LUSTER SAMPLING: A POPULATION IS DIVIDED INTO*.$LUSTER SAMPLING: A POPULATION IS DIVIDED INTO

$LUSTERS USING NATURALL% O$$URING GEOGRAPHI$ OR$LUSTERS USING NATURALL% O$$URING GEOGRAPHI$ OROTHER BOUNDARIES. THEN= $LUSTER ARE RANDOML%OTHER BOUNDARIES. THEN= $LUSTER ARE RANDOML%SELE$TED AND A SAMPLE IS $OLLE$TED B% RANDOML%SELE$TED AND A SAMPLE IS $OLLE$TED B% RANDOML%SELE$TING FROM EA$H $LUSTER.SELE$TING FROM EA$H $LUSTER.


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S,+C9 M574oS,+C9 M574o

P+p.-8e +a'm .ampl-'9P+p.-8e +a'm .ampl-'9 P+p+)-'al +a'm .ampl-'9P+p+)-'al +a'm .ampl-'9

N'Ra'm .ampl-'9N'Ra'm .ampl-'9 C'8e'-e'/e .ampl-'9C'8e'-e'/e .ampl-'9

9me') .ampl-'99me') .ampl-'9 S'(all .ampl-'9S'(all .ampl-'9


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SAMPLIN DISTRIBUTION OF THE SAMPLE MEANSAMPLIN DISTRIBUTION OF THE SAMPLE MEAN

SAMPLIN DISTRIBUTION OF THE SAMPLE MEAN IS ASAMPLIN DISTRIBUTION OF THE SAMPLE MEAN IS APROBABILITY DISTRIBUTION OF ALL POSSIBLEPROBABILITY DISTRIBUTION OF ALL POSSIBLESAMPLE MEANS OF A IVEN SAMPLE SIGE : ' ;2SAMPLE MEANS OF A IVEN SAMPLE SIGE : ' ;2

THE FOLLO>IN EXAMPLE ILLUSTRATES THETHE FOLLO>IN EXAMPLE ILLUSTRATES THECONTRUCTION OF A SAMPLIN DISTRIBUTION OFCONTRUCTION OF A SAMPLIN DISTRIBUTION OFSAMPLE MEAN2SAMPLE MEAN2

LET US ASSUME THAT A POPULATION CONSISTS OFLET US ASSUME THAT A POPULATION CONSISTS OFFOUR ELEMENTS X1 ?1, X! ? !, X" ? " AND X% ? %2FOUR ELEMENTS X1 ?1, X! ? !, X" ? " AND X% ? %2CONSIDER ALL THE SAMPLES OF A IVEN SIGE ' ? !CONSIDER ALL THE SAMPLES OF A IVEN SIGE ' ? !

THAT COULD BE DRA>N FROM THIS POPULATION2THAT COULD BE DRA>N FROM THIS POPULATION2:CONSIDER CAREFULLY >HETHER ONE IS SAMPLIN:CONSIDER CAREFULLY >HETHER ONE IS SAMPLIN>ITH OR >ITHOUT REPLACEMENT;2>ITH OR >ITHOUT REPLACEMENT;2


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Sampl-'9 -)* Repla/eme')Sampl-'9 -)* Repla/eme')A Co15 A Co15A Co15 A Co15

,+C5 ,+C5 +5,9 ,+C5 ,+C5 +5,9,+C5 ,+C5 +5,9 ,+C5 ,+C5 +5,9

(. (.( (.& !. .( #.&(. (.( (.& !. .( #.&

#. (.# (.) (&. .# #.)#. (.# (.) (&. .# #.)

. (. #.& ((. . .&. (. #.& ((. . .&

*. (.* #.) (#. .* .)*. (.* #.) (#. .* .)

). #.( (.) (. *.( #.)). #.( (.) (. *.( #.)>. #.# #.& (*. *.# .&>. #.# #.& (*. *.# .&

. #. #.) (). *. .). #. #.) (). *. .)

' #.* .& (>. *.* *.&' #.* .& (>. *.* *.&

? @ ( # * : * ? #.) @ CoC0,7o9 +5,9 ? @ ( # * : * ? #.) @ CoC0,7o9 +5,9 6 ? @ ( (.) #.& ------------- *.& : (> ? #.) T45 +5,9 of , 745 +5,96 ? @ ( (.) #.& ------------- *.& : (> ? #.) T45 +5,9 of , 745 +5,9

50, 7o 745 CoC0,7o9 +5,9 or 50, 7o 745 CoC0,7o9 +5,9 or ..


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V,r,9c5 ,9 S7,9,r D5,7o9V,r,9c5 ,9 S7,9,r D5,7o9

##? @ ( #.) ? @ ( #.) ##@ # #.) @ # #.) ## @ #.) @ #.) ## @ * #.) @ * #.) ##: *: *?? @ #.#) &.#) &.#) #.#): * ? )/*@ #.#) &.#) &.#) #.#): * ? )/* ++ ##? )/* ? (.#)? )/* ? (.#)

? 7 12!5 ? 1211 : .) e8-a)-' 3 ppla)-';? 7 12!5 ? 1211 : .) e8-a)-' 3 ppla)-';T*e .)a'a+ e8-a)-' 3 )*e .ample mea'. -. 3+mall4 +e3e++eT*e .)a'a+ e8-a)-' 3 )*e .ample mea'. -. 3+mall4 +e3e++e

a. .)a'a+ e+++ 3 )*e mea'2a. .)a'a+ e+++ 3 )*e mea'266##??@ ( -#.) @ ( -#.) ## @ (.) #.) @ (.) #.) ##------------------------- @ * #.) ------------------------- @ * #.) ## : (>: (>

? 10 & 1# ? 02#!5 a'? 10 & 1# ? 02#!5 a' x ? 7 02#!5 ? 02$ +x ? 7 02#!5 ? 02$ + 1211 1211

x ? ? ? 02$x ? ? ? 02$ 77 ' 7 !' 7 !N)e )*a) *e' e -'/+ea.e ', )*eN)e )*a) *e' e -'/+ea.e ', )*e x -ll e/+ea.e2x -ll e/+ea.e2


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>-)*) Repla/eme')>-)*) Repla/eme')

A Co15 ,+C5 S,+C5 +5,9A Co15 ,+C5 S,+C5 +5,9

(.# (.)(.# (.)

(. #.&(. #.&

(.* #.)(.* #.)

#. #.)#. #.)

#.* ..* .&

.* .).* .)6 ? @ (.) #.& ------- .) : > ? #.)6 ? @ (.) #.& ------- .) : > ? #.)

6# ? @ (.) #.) # @ #.& #.) # ----- @ .) #.)# : >6# ? @ (.) #.) # @ #.& #.) # ----- @ .) #.)# : >

? @( &.#) & & &.#) ( ? #.) : > ? &.*(? @( &.#) & & &.#) ( ? #.) : > ? &.*(

6 ? X &.*( ? &.>*) or6 ? X &.*( ? &.>*) or 6 ? --- @ X @ N 9 : @ N ( 6 ? --- @ X @ N 9 : @ N (

XX 99


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Example&Example& Sampl-'9 D-.)+-()-' 3 T*e Mea'Sampl-'9 D-.)+-()-' 3 T*e Mea'

A ppla)-' /'.-.). 3 )*+ee eleme').&A ppla)-' /'.-.). 3 )*+ee eleme').&X1 ? !5, X!? "0 a' X" ? "52X1 ? !5, X!? "0 a' X" ? "52

Cal/la)e&Cal/la)e&

a2a2 Sampl-'9 -.)+-()-' 3 )*e mea' -3 )*eSampl-'9 -.)+-()-' 3 )*e mea' -3 )*e.ample .-e ? ! : -)* +epla/eme') a'.ample .-e ? ! : -)* +epla/eme') a'-)*) +epla/eme') ;2-)*) +epla/eme') ;2

(2 Va+-a'/e a' .) e8-a)-' 3 )*e .ample(2 Va+-a'/e a' .) e8-a)-' 3 )*e .amplemea'.2mea'.2


45/87


46/87

1212 C'3-e'/e -')e+8al 3+ )*e ppla)-' mea' :C'3-e'/e -')e+8al 3+ )*e ppla)-' mea' : ;;*e' ' "0 : G 8ale ;*e' ' "0 : G 8ale ;

C'3-e'/e -')e+8al 3+C'3-e'/e -')e+8al 3+ -. e.)-ma)e (4&-. e.)-ma)e (4&

XX QQ a .ampl-'9 e+++ + Xa .ampl-'9 e+++ + X QQ 8ale SE 8ale SE

G 8ale epe'. ' /'3-e'/e le8el2G 8ale epe'. ' /'3-e'/e le8el2SE ? .)a'a+ e+++ 3 )*e mea'SE ? .)a'a+ e+++ 3 )*e mea'

SE ?SE ? 7', -3 .) e8-a)-' 3 ppla)-' -. ''27', -3 .) e8-a)-' 3 ppla)-' -. ''2

B), -3 )*e .) e8-a)-' 3 ppla)-' -. ''',B), -3 )*e .) e8-a)-' 3 ppla)-' -. ''',SE ? .7' , . ? .) e8-a)-' 3 .ample2SE ? .7' , . ? .) e8-a)-' 3 .ample2


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Sampl-'9 E+++ a' C'3-e'/e I')e+8al E.)-ma)eSampl-'9 E+++ a' C'3-e'/e I')e+8al E.)-ma)e S,+C9 Error : T45 ffr59c5 157559 , ,+C5S,+C9 Error : T45 ffr59c5 157559 , ,+C5

7,77c ,9 7 corr5Co99 CoC0,7o9 C,r,+575r.7,77c ,9 7 corr5Co99 CoC0,7o9 C,r,+575r.T4 5rror 5cr5,5 , 745 ,+C5 5 9cr5,5.T4 5rror 5cr5,5 , 745 ,+C5 5 9cr5,5.

$o9f59c5 975r, 57+,75: A r,95 of ,05$o9f59c5 975r, 57+,75: A r,95 of ,05

co97r0c75 fro+ ,+C5 ,7, o 74,7 745 CoC0,7o9co97r0c75 fro+ ,+C5 ,7, o 74,7 745 CoC0,7o9C,r,+575r 853 7o 749 74,7 r,95 occ0r ,7C,r,+575r 853 7o 749 74,7 r,95 occ0r ,7C5cf5 Cro1,173. T45 C5cf5 Cro1,173 C5cf5 Cro1,173. T45 C5cf5 Cro1,173 c,5 745 55 of co9f59c5.c,5 745 55 of co9f59c5.


48/87

EXAMPLE&EXAMPLE& C'3-e'/e I')e+8al 3+C'3-e'/e I')e+8al 3+ : '"0: '"0;;

T45 +5,9 ,9 7 5,7o9 for 745 0,73 r,5T45 +5,9 ,9 7 5,7o9 for 745 0,73 r,5Co97 ,5r,5 of , r,9o+ ,+C5 of > co55Co97 ,5r,5 of , r,9o+ ,+C5 of > co5559or ,r5 c,c0,75 7o 15 #.! ,9 &.59or ,r5 c,c0,75 7o 15 #.! ,9 &.

r5C5c753.r5C5c753.,. F9 745 !# co9f59c5 975r, for 745 +5,9 of,. F9 745 !# co9f59c5 975r, for 745 +5,9 of745 597r5 59or c,.745 597r5 59or c,.

1. Ho ,r5 745 ,+C5 5 r50r5 f 5 ,971. Ho ,r5 745 ,+C5 5 r50r5 f 5 ,977o r50c5 745 ,+C9 5rror 9o7 +or5 74,9 &.&).7o r50c5 745 ,+C9 5rror 9o7 +or5 74,9 &.&).


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C'3-e'/e I')e+8al 3+C'3-e'/e I')e+8al 3+ : ' "0 ;: ' "0 ;

T45 547 of +,r 1o65 of c5r5, ,r5 !.'= (&.#= (&.*=T45 547 of +,r 1o65 of c5r5, ,r5 !.'= (&.#= (&.*=!.'= (&.&= (&.# ,9 !.> o09c5.!.'= (&.&= (&.# ,9 !.> o09c5.

F9 , !& co9f59c5 975r, for 45 +5,9 of , 0c4 1o65F9 , !& co9f59c5 975r, for 45 +5,9 of , 0c4 1o65

of c5r5,. @ 05 7 7,15 .of c5r5,. @ 05 7 7,15 .S75CS75C((: c,c0,75 745 +5,9 ,9 7 5,7o9 of ,+C5.: c,c0,75 745 +5,9 ,9 7 5,7o9 of ,+C5.

#: 05 7 7,15 7o f9 cr7c, ,05 for !& $.L @ 7.#: 05 7 7,15 7o f9 cr7c, ,05 for !& $.L @ 7.

: 0177075 of , 9for+,7o9 fro+ 75C ( ,9 #: 0177075 of , 9for+,7o9 fro+ 75C ( ,9 #

97o 745 for+0,:97o 745 for+0,:

< - 7 @ /< - 7 @ /X9 0 < 7 @ /X9 X9 0 < 7 @ /X9


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Le8el 3 C'3-e'/eLe8el 3 C'3-e'/eR50r5 55 ,05 ofR50r5 55 ,05 of YY ,05 of 7,15 ,05 of 7,15

of co9f59c5of co9f59c5!& (& !& (& ZZ(.>)(.>)

!) ) !) ) ZZ(.!>(.!>

!! ( !! ( ZZ#.)'#.)'E6,+C5 : T45 Crc5 ,7 4c4 c5r7,9 73C5 of 97,97 coff55 ,E6,+C5 : T45 Crc5 ,7 4c4 c5r7,9 73C5 of 97,97 coff55 ,159 o o9 , 59 ,3 5r5 co5c75 fro+ , r,9o+159 o o9 , 59 ,3 5r5 co5c75 fro+ , r,9o+,+C5 of *) 4oC ,ro09 745 co097r3. T45 +5,9 Crc5 , [,+C5 of *) 4oC ,ro09 745 co097r3. T45 +5,9 Crc5 , [(.!) 74 , 7,9,r 5,7o9 of [ &.#. $o+C075 , '& (.!) 74 , 7,9,r 5,7o9 of [ &.#. $o+C075 , '& co9f59c5 975r, for 745 CoC0,7o9 +5,9.co9f59c5 975r, for 745 CoC0,7o9 +5,9.


51/87

A A 7


52/87

ACCc,7o9ACCc,7o9

T*e -.)+-()-' 3 *.e*l )*a) 3a8+ a /e+)a-' (a)* .ap -'T*e -.)+-()-' 3 *.e*l )*a) 3a8+ a /e+)a-' (a)* .ap -'>e.) a8a P+8-'/e :.e a 0 /'3-e'/e le8el;2>e.) a8a P+8-'/e :.e a 0 /'3-e'/e le8el;2

B+a' Nm(e+ 3 *.e*l.B+a' Nm(e+ 3 *.e*l. Palml-8e 1500Palml-8e 1500 Lx 100Lx 100 Ge.) 1500Ge.) 1500 Bea)4 1000Bea)4 1000 M-')4 1!00M-')4 1!00 O)*e+ (+a'. !000O)*e+ (+a'. !000 Cal/la)e /'3-e'/e -')e+8al 3+ )*e p+p+)-' 3 *.e*l.Cal/la)e /'3-e'/e -')e+8al 3+ )*e p+p+)-' 3 *.e*l.

)*a) 3a8+ LUX (a)* .ap 3+ )*e-+ 3am-l-e.2)*a) 3a8+ LUX (a)* .ap 3+ )*e-+ 3am-l-e.2


53/87


54/87

F-'-'9 ) 8aleF-'-'9 ) 8ale

Example & ' ? 10, /'3-e'/e le8el ? 02Example & ' ? 10, /'3-e'/e le8el ? 02 ' ? !%, /'3-e'/e le8el ? 5' ? !%, /'3-e'/e le8el ? 5

De9+ee 3 3+eem 3 ) 8ale ? 3 :'1 ;De9+ee 3 3+eem 3 ) 8ale ? 3 :'1 ;3 T)a-le )e.),3 T)a-le )e.),WW )8ale )8ale

1010 QQ12""12""

!" 5!" 5 QQ!20#!20#


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"2"2 A /'3-e'/e I')e+8al 3+ T*e -33+e'/e (e)ee' TA /'3-e'/e I')e+8al 3+ T*e -33+e'/e (e)ee' TPpla)-' Mea'. :Ppla)-' Mea'. : 1 1 ! ;, ' "0! ;, ' "0

$o9f59c5 975r, for 745 ffr59c5 157559$o9f59c5 975r, for 745 ffr59c5 157559 ( -( - # :# :

@


56/87

E6,+C5E6,+C5

A 703 , +,5 7o 57+,75 745 ff5r59c5 9 ,,r5A 703 , +,5 7o 57+,75 745 ff5r59c5 9 ,,r5

of co55 Crof5or 9 745 Cr,75 ,9 7,75 co55of co55 Crof5or 9 745 Cr,75 ,9 7,75 co55of Vr9,. A r,9o+ ,+C5 of (&& Crof5or 9 745of Vr9,. A r,9o+ ,+C5 of (&& Crof5or 9 745Cr,75 co55 4o5 ,9 ,5r,5 of [ ().&&& C5rCr,75 co55 4o5 ,9 ,5r,5 of [ ().&&& C5r+o974 74 , 7,9,r 5,7o9 of [ (#&&. A r,9o++o974 74 , 7,9,r 5,7o9 of [ (#&&. A r,9o+

,+C5 of #&& Crof5or 9 7,75 co55 4o5 ,9,+C5 of #&& Crof5or 9 7,75 co55 4o5 ,9,5r,5 ,,r3 of [ (>.&&& 74 , 7,9,r 5,7o9,5r,5 ,,r3 of [ (>.&&& 74 , 7,9,r 5,7o9of [of [ ((*&&. F9 , !& co9f59c5 975r, for 745*&&. F9 , !& co9f59c5 975r, for 745ff5r59c5 157559 745 ,5r,5 ,,r5 of Crof5orff5r59c5 157559 745 ,5r,5 ,,r5 of Crof5or

75,c49 9 7,75 ,9 Cr,75 co55 9 Vr9,.75,c49 9 7,75 ,9 Cr,75 co55 9 Vr9,.


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5252 E.)-ma)-'9 )*e -33e+e'/e (e)ee' ) ppla)-'E.)-ma)-'9 )*e -33e+e'/e (e)ee' ) ppla)-'mea'. :mea'. : 11 ! ;, ' "0! ;, ' "0

@@


58/87

EXAMPLE& POPULATION PROPORTIONEXAMPLE& POPULATION PROPORTION

A 'e p+9+am 3+ a 4)* /l( -. pla''e -' a .mall /-)42 TA 'e p+9+am 3+ a 4)* /l( -. pla''e -' a .mall /-)42 Te)e+m-'e *e)*e+ + ') )*e p+9+am -ll 9e) )*e /-)4e)e+m-'e *e)*e+ + ') )*e p+9+am -ll 9e) )*e /-)498e+'me')6. .pp+)2 I) -. 'e/e..a+4 ) e.)-ma)e )*e p+p+)-'98e+'me')6. .pp+)2 I) -. 'e/e..a+4 ) e.)-ma)e )*e p+p+)-'3 4'9 peple * pla' ) .e )*e /l(6. 3a/-l-)-e.2 A .+8e4 33 4'9 peple * pla' ) .e )*e /l(6. 3a/-l-)-e.2 A .+8e4 3

100 +a'ml4 .ele/)e 4'9 peple *a. .*' )*a) !! -ll .e100 +a'ml4 .ele/)e 4'9 peple *a. .*' )*a) !! -ll .e)*e 3a/-l-)-e. -3 )*e4 (e/me a8a-la(le2 C'.)+/) a 0)*e 3a/-l-)-e. -3 )*e4 (e/me a8a-la(le2 C'.)+/) a 0/'3-e'/e -')e+8al 3+ )*e )+e p+p+)-'2/'3-e'/e -')e+8al 3+ )*e )+e p+p+)-'2

' ? 100, X ? !!, P ? !!100 ? 02!! a' : 1 P ; ? 02$' ? 100, X ? !!, P ? !!100 ? 02!! a' : 1 P ; ? 02$

G 8ale 3+ CL ? 0 ?G 8ale 3+ CL ? 0 ? QQ12#5212#52


59/87

Example&Example&

T45 C5rfor+,9c5 of 7oc8 157559 $5+597T45 C5rfor+,9c5 of 7oc8 157559 $5+597I907r5 ,9 O 907r5 9 #&& @ 9 .I907r5 ,9 O 907r5 9 #&& @ 9 . $5+597 I907r5 O I907r5$5+597 I907r5 O I907r5 A5r,5 35 ## ('A5r,5 35 ## (' V,r,9c5 #V,r,9c5 # S,+C5 5 ) *&S,+C5 5 ) *&

$,c0,75 975r, 57+,75 745 ff5r59c5 9 ,5r,5$,c0,75 975r, 57+,75 745 ff5r59c5 9 ,5r,535 157559 c5+597 907r5 ,9 o 907r535 157559 c5+597 907r5 ,9 o 907r5@ $L ? ') .@ $L ? ') .

* R $


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0 * : R5r5o9 ,9 $orr5,7o90 * : R5r5o9 ,9 $orr5,7o9M-)e+m 9+ae. F-'al 9+ae.M-)e+m 9+ae. F-'al 9+ae.

$$$$ ! !5050 ## ##

$1 $$1 $

$! 0$! 0

!! 5 5

a2 C'.)+/) )*e +e9+e..-' l-'e (4 .-'9 OLS2a2 C'.)+/) )*e +e9+e..-' l-'e (4 .-'9 OLS2

(2 Cal/la)e R a' R .=a+e2(2 Cal/la)e R a' R .=a+e2/2 >*e' 4 9) ./+e $5 -' m-exam, *a) -. 4+ p+e-/)-'/2 >*e' 4 9) ./+e $5 -' m-exam, *a) -. 4+ p+e-/)-'

./+e -' 3-'alexam


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H3Co7455 7579H3Co7455 7579


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TESTIN HYPOTHESESTESTIN HYPOTHESES : CH& 10 P 11#5!1;: CH& 10 P 11#5!1;

H%POTHESIS TESTING: A PRO$EDURE BASED ONH%POTHESIS TESTING: A PRO$EDURE BASED ONSAMPLE EVIDEN$E TO DETERMINE WHETHER THESAMPLE EVIDEN$E TO DETERMINE WHETHER THEH%POTHESIS IS A REASONABLE STATEMENT.H%POTHESIS IS A REASONABLE STATEMENT.

H%POTHESIS: A STATEMENT ABOUT A POPULATIONH%POTHESIS: A STATEMENT ABOUT A POPULATIONDEVELOPED FOR THE PURPOSE OF TESTING.DEVELOPED FOR THE PURPOSE OF TESTING.

NULL H%POTHESIS @ Ho : SPE$IFIES THE VALUE OFNULL H%POTHESIS @ Ho : SPE$IFIES THE VALUE OFTHE PARAMETER TO BE TESTED. 5.:THE PARAMETER TO BE TESTED. 5.: == QQ= @ (- # OR= @ (- # ORH%POTHESES THAT WE FORMULATE WITH THEH%POTHESES THAT WE FORMULATE WITH THEHOPE OF REJE$TING.HOPE OF REJE$TING.

ALTERNATIVE H%POTHESIS @ H, : H%POTHESESALTERNATIVE H%POTHESIS @ H, : H%POTHESESTHAT WE FORMULATE WITH THE HOPE OFTHAT WE FORMULATE WITH THE HOPE OFA$$EPTING.A$$EPTING.


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H%POTHESIS TESTING PRO$EDUREH%POTHESIS TESTING PRO$EDURE

TWO-TAILED TEST: BASI$ALL% BE USED TOTWO-TAILED TEST: BASI$ALL% BE USED TOTEST IF THE UESTION ASK %OU ABOUT:TEST IF THE UESTION ASK %OU ABOUT:THE DIFFEREN$E= $HANGE OR EFFE$T.THE DIFFEREN$E= $HANGE OR EFFE$T.

@ ALPHA IS DIVIDED B% # OR@ ALPHA IS DIVIDED B% # OR ZZ (/#(/#YY ONE TAILED TEST : BASI$ALL% BE USED TOONE TAILED TEST : BASI$ALL% BE USED TO

TEST IF THE UESTION ASK %OU ABOUT:TEST IF THE UESTION ASK %OU ABOUT:GREATER THAN= LESS THAN= IN$REASE=GREATER THAN= LESS THAN= IN$REASE=

DE$REASE= OR MORE THAN. THE $RITI$ALDE$REASE= OR MORE THAN. THE $RITI$ALSTATISTI$ TABLE MA% BE IN THE LEFT ORSTATISTI$ TABLE MA% BE IN THE LEFT ORIN THE RIGHT TAIL OF THE $URVE.IN THE RIGHT TAIL OF THE $URVE.


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THE ENERAL PROCEDURE FOR A HYPOTHESIS TESTTHE ENERAL PROCEDURE FOR A HYPOTHESIS TEST

START S7,75 745 Ho ,9 H, @ 7o or o95 7,5 757 START S7,75 745 Ho ,9 H, @ 7o or o95 7,5 757

S55c7 745 5r5 $L or ,C4,S55c7 745 5r5 $L or ,C4,

D575r+95 745 cr7c, 7,15 @ = 7= F or 6D575r+95 745 cr7c, 7,15 @ = 7= F or 6##

D575r+95 745 r55c7o9 ,9 ,cc5C7,9c5 ,r5, of Ho.D575r+95 745 r55c7o9 ,9 ,cc5C7,9c5 ,r5, of Ho.

$o+C075 745 cr7c, r,7o 13 09 ,7, ,+C5 @ 757-7,77c $o+C075 745 cr7c, r,7o 13 09 ,7, ,+C5 @ 757-7,77c

$o+C,r5 745 cr7c, r,7o ,9 7,15 @ ,cc5C7 or r55c7 Ho $o+C,r5 745 cr7c, r,7o ,9 7,15 @ ,cc5C7 or r55c7 Ho

$o9c0o9$o9c0o9


65/87

12Te.)-'9 )*e Ppla)-' Mea' :12Te.)-'9 )*e Ppla)-' Mea' : ;, ' "0 ;, ' "0

Example& M+ X, a m)*a.* -.)+-()+, *a. .)a)e )*a) )*eExample& M+ X, a m)*a.* -.)+-()+, *a. .)a)e )*a) )*ea8e+a9e /.) ) p+/e.. a .ale. +e+ -. @ 1",!52 M-.. Y, /.)a8e+a9e /.) ) p+/e.. a .ale. +e+ -. @ 1",!52 M-.. Y, /.)/')+lle+, 3ea+. )*a) )*e a8e+a9e /.) 3 p+/e..-'9 -. m+e/')+lle+, 3ea+. )*a) )*e a8e+a9e /.) 3 p+/e..-'9 -. m+e)*a' @1"2!52 S*e -. -')e+e.)e -' )a-'9 a/)-' -3 /.) a+e *-9*,)*a' @1"2!52 S*e -. -')e+e.)e -' )a-'9 a/)-' -3 /.) a+e *-9*,

() .*e e. ') /a+e -3 )*e a/)al a8e+a9e /.) -. (el )*e() .*e e. ') /a+e -3 )*e a/)al a8e+a9e /.) -. (el )*ea..me 8ale2 A +a'm .ample 3 100 +e+. *a a .amplea..me 8ale2 A +a'm .ample 3 100 +e+. *a a .amplemea' 3 @1"2"5, a..m-'9 )*e .) e8-a)-' -. @ 02502mea' 3 @1"2"5, a..m-'9 )*e .) e8-a)-' -. @ 02502 ConductConducta test at 5 % level of significance and can you conclude thata test at 5 % level of significance and can you conclude that

the average cost of a sales order is more than $13.25?the average cost of a sales order is more than $13.25?


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TEST STATISTI$ FORTEST STATISTI$ FOR @ 9 & @ 9 &

H?H? Ha?Ha? CRITICAL VALUES : G TABLE ;CRITICAL VALUES : G TABLE ; ACCEPTANCE REECTION AREASACCEPTANCE REECTION AREAS TEST STATISTIC& X TEST STATISTIC& X G* ? G* ? SD7'SD7'2 TEST STATISTIC IS FOUND FROM SAMPLE2 TEST STATISTIC IS FOUND FROM SAMPLE

INFORMATION2INFORMATION22 DECISION& ACCEPT OR REECT H22 DECISION& ACCEPT OR REECT H22 CONCLUSION&2 CONCLUSION&

# TEST STATISTI$ FOR# TEST STATISTI$ FOR QQ


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#. TEST STATISTI$ FOR#. TEST STATISTI$ FOR QQ@POPULATION PROPORTION@POPULATION PROPORTION

TEST STATISTIC&TEST STATISTIC&

P P

G* ? G* ? : 1 : 1 ;';'

TESTING FOR A PROPORTIONTESTING FOR A PROPORTION


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TESTING FOR A PROPORTIONTESTING FOR A PROPORTIONPOPULATIONPOPULATION

RESEARCH AT THE UM INDICATES THAT 50RESEARCH AT THE UM INDICATES THAT 50OF THE STUDENTS CHANE THEIR MAOR OFOF THE STUDENTS CHANE THEIR MAOR OFSTUDY AFTER THEIR FIRST YEAR IN ASTUDY AFTER THEIR FIRST YEAR IN APRORAM2 A RANDOM SAMPLE OF 100PRORAM2 A RANDOM SAMPLE OF 100

STUDENTS IN THE BUSINESS PRORAMSTUDENTS IN THE BUSINESS PRORAMREVEALED THAT % HAD CHANED THEIRREVEALED THAT % HAD CHANED THEIRMAOR AREA OF STUDY AFTER THEIR FIRSTMAOR AREA OF STUDY AFTER THEIR FIRSTYEAR OF THE PRORAM2YEAR OF THE PRORAM2Has there been aHas there been a

significant decrease in the proportion of students hosignificant decrease in the proportion of students hochange their ma!or after the first year in this program?change their ma!or after the first year in this program?"est at the #.#5 level of significance."est at the #.#5 level of significance.


69/87

E6,+C5:#E6,+C5:#Br,9 of 1,74 o,C N0+15r of Ho054oBr,9 of 1,74 o,C N0+15r of Ho054o

P,+o5 (&&&P,+o5 (&&&L06 ()&&L06 ()&&

57 (&&&57 (&&&

B5,073 )&B5,073 )&

M973 (#)&M973 (#)&

M,3, (&&&M,3, (&&&

O745r Br,9 )&&O745r Br,9 )&&

,.,.

$,9 3o0 co9c05 74,7 745 CroCor7o9 of HH 74,7 85 L06 $,9 3o0 co9c05 74,7 745 CroCor7o9 of HH 74,7 85 L06 ff5r597 fro+ (*.ff5r597 fro+ (*.

1.1. $,9 3o0 co9c05 74,7 745 CroCor7o9 of HH 74,7 85 L06 $,9 3o0 co9c05 74,7 745 CroCor7o9 of HH 74,7 85 L06 445r 74,9 (* . @ AC4, ? () .445r 74,9 (* . @ AC4, ? () .

5 T )- T* P l )- M :5 T )- T* P l )- M : ; "0; "0


70/87

52 Te.)-'9 T*e Ppla)-' Mea' :52 Te.)-'9 T*e Ppla)-' Mea' : ;, ' "0 ;, ' "0: U.e ))a(le ;: U.e ))a(le ;p& $5p& $5

T57 S7,77c:T57 S7,77c: < -< -

74 ? ------------74 ? ------------

SD / 9SD / 9

ExampleExample


71/87

ExampleExample

T45 7r107o9 of ,o95 co90+C7o9 of > ,+C5T45 7r107o9 of ,o95 co90+C7o9 of > ,+C5Ho9, A7r5, c,9 15 r5Cor75 , foo:Ho9, A7r5, c,9 15 r5Cor75 , foo:S,+C5 R,95S,+C5 R,95

( )* 8+/( )* 8+/ # )# )

)> )>

* )#* )# ) )&) )&

> ))> ))

T45 +,90f,c70r5 c,+5 74,7 745 ,5r,5 of ,o95T45 +,90f,c70r5 c,+5 74,7 745 ,5r,5 of ,o95

$o90+C7o9 , )) 8+/.$o90+C7o9 , )) 8+/. Cn #o) %on%")*e t$t t$&+ %"&, &+Cn #o) %on%")*e t$t t$&+ %"&, &+oere+t&,te / )+e "!$ 0 1 2 3.oere+t&,te / )+e "!$ 0 1 2 3.

TESTING THE DIFFEREN$E BETWEEN TWOTESTING THE DIFFEREN$E BETWEEN TWO


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TESTING THE DIFFEREN$E BETWEEN TWOTESTING THE DIFFEREN$E BETWEEN TWOPOPULATION MEANSPOPULATION MEANS

PARAMETRI$ STATISTI$S:PARAMETRI$ STATISTI$S: (. SPSS: PAIRED SAMPLES(. SPSS: PAIRED SAMPLES #. EVIEWS: UNPAIRED SAMPLES:#. EVIEWS: UNPAIRED SAMPLES:

EUALIT% OF VARIAN$E TESTEUALIT% OF VARIAN$E TEST . E


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.TEST STATISTI$ FOR @.TEST STATISTI$ FOR @( -#= 9 &( -#= 9 &@I95C59597-,+C5 757 @I95C59597-,+C5 757

H&H& Ha&Ha& TEST STATISTIC&TEST STATISTIC& X1 X!X1 X! G* ? G* ?

8a+1'1 8a+!'!8a+1'1 8a+!'!


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EXAMPLEEXAMPLE THE PRODU$TION OF ELE$TRONI$ ITEMS DAIL% INTHE PRODU$TION OF ELE$TRONI$ ITEMS DAIL% IN

$OMPAN% AB$:$OMPAN% AB$: MALE WOKERS FEMALE WORKERSMALE WOKERS FEMALE WORKERS

AVERAGE PROD *)& UNITS *>& UNITSAVERAGE PROD *)& UNITS *>& UNITS

VARIAN$E !& UNITS ((& UNITSVARIAN$E !& UNITS ((& UNITS

SAMPLE SIE *& WORKERS )& WORKERSSAMPLE SIE *& WORKERS )& WORKERS

$AN %OU $ON$LUDE THAT THE AVERAGE OF$AN %OU $ON$LUDE THAT THE AVERAGE OFFEMALE WORKERS PRODU$TIVIT% IS HIGHERFEMALE WORKERS PRODU$TIVIT% IS HIGHERTHAN MALE WORKERSTHAN MALE WORKERS

@ USE ALPHA ? (& @ USE ALPHA ? (&


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*:To S,+C5 757 ,1o07 ProCor7o9 @*:To S,+C5 757 ,1o07 ProCor7o9 @ QQ( ( QQ# #

A r,9o+ ,+C5 of (&& 3o09 o+59 r55,5 (! 85A r,9o+ ,+C5 of (&& 3o09 o+59 r55,5 (! 85

745 H5,593 frr,9c5 5 59o04 7o C0rc4,5 7.745 H5,593 frr,9c5 5 59o04 7o C0rc4,5 7.S+,r3= , ,+C5 of #&& o5r o+59 r55,5 ># 85S+,r3= , ,+C5 of #&& o5r o+59 r55,5 ># 85745 fr,r,9c5 5 59o04 7o +,85 , C0rc4,5.745 fr,r,9c5 5 59o04 7o +,85 , C0rc4,5. Cn #o)Cn #o)%on%")*e t$t t$ere &+ *&fferen%e &n t$e !ro!ort&on of%on%")*e t$t t$ere &+ *&fferen%e &n t$e !ro!ort&on of

#o)nger n* o"*er 4o,en 4$o "&(e t$e 5een"##o)nger n* o"*er 4o,en 4$o "&(e t$e 5een"# fr,r,9c5fr,r,9c5@ ,C4, ? ).@ ,C4, ? ).

Poo5 ,+C5 CroCor7o9 Pc ? @


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>.TEST STATISTI$ FOR @>.TEST STATISTI$ FOR @( - #= 9 \ &( - #= 9 \ &@ USE- 7 TABLE @ USE- 7 TABLE

TEST STATISTIC&TEST STATISTIC& X1 X!X1 X! )* ? )* ? : '11; 8a+1 :'!1; 8a+! 1 1: '11; 8a+1 :'!1; 8a+! 1 1 :'1 '! !; '1 '!:'1 '! !; '1 '!


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. D5C59597 S,+C5 757


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. D5C59597 S,+C5 757S,+C5 Pro0c773 of Wor85r Af75r Tr,99 B5for5 Tr,99 @ - @ #

( #) 097 ##' 097 #.* ).># #(& #&) ) &.* &.(> #( #(! (# .* )*.>* #*# #*& # -#.> >.>) #&) (!' #.* ).>> #& ## #.* ).> #( ## * -&.> &.>' #(& #() -) -!.> !#.(>! ##) ### -(.> #.)>

(& #*! #*) * -&.> &.> $,9 3o0 co9c05 74,7 745 7r,99 Cror,+ 9cr5,5 745Cro0c773 of 745 5+Co355 @ ,C4, ? ) .


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& CHY SJUARE TEST& CHY SJUARE TEST


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& CHY SJUARE TEST& CHY SJUARE TESTTa(le& p& $$Ta(le& p& $$

C*4 .=a+e )e.). a+e .e -' a p+/e+e )*a)C*4 .=a+e )e.). a+e .e -' a p+/e+e )*a)-'8l8e. )*e /mpa+-.' 3 )*e -33e+e'/e. (e)ee'-'8l8e. )*e /mpa+-.' 3 )*e -33e+e'/e. (e)ee')*e .ample 3+e=e'/-e. 3 )*e //++e'/e : O- ; a')*e .ample 3+e=e'/-e. 3 )*e //++e'/e : O- ; a')*e *4p)*e)-/al + )*e+e)-/al ppla)-' 3+e=e'/-e.)*e *4p)*e)-/al + )*e+e)-/al ppla)-' 3+e=e'/-e.

: E- ; : Expe/)e 8ale ;2 : 'e.. 3 F-) ;2: E- ; : Expe/)e 8ale ;2 : 'e.. 3 F-) ;2 I) /a' al. (e .e ) )e.) +ela)-'.*-p (e)ee'I) /a' al. (e .e ) )e.) +ela)-'.*-p (e)ee'

8a+-a(le. : -'epe'e'/4 )e.) ;28a+-a(le. : -'epe'e'/4 )e.) ;2 C+-)-/al 8ale 3 xC+-)-/al 8ale 3 x!!epe'. ' )*e 'm(e+ 3 +.epe'. ' )*e 'm(e+ 3 +.

a' /lm'.a' /lm'.


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$43 0,r5 7,15$43 0,r5 7,15

C*4 .=a+e )a(le -. ala4. 'e )a-le -' )*eC*4 .=a+e )a(le -. ala4. 'e )a-le -' )*e+-9*) .-e 3 )*e /+8e2+-9*) .-e 3 )*e /+8e2

C+-)-/al )a(le -. XC+-)-/al )a(le -. X##ZZ3 : + 1 ;: / 1 ;23 : + 1 ;: / 1 ;2 H -. a//ep)e -3 )e.) .)a)-.)-/. /al/la)e -.H -. a//ep)e -3 )e.) .)a)-.)-/. /al/la)e -.

le.. )*a' + e=al ) -). /+-)-/al )a(le2le.. )*a' + e=al ) -). /+-)-/al )a(le2 H -. +ee/)e -3 )e.) .)a)-.)-/. /al/la)e -.H -. +ee/)e -3 )e.) .)a)-.)-/. /al/la)e -.

9+ea)e+ )*a' -). /+-)-/al )a(le29+ea)e+ )*a' -). /+-)-/al )a(le2


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C*4S=a+e )e.)C*4S=a+e )e.)

Te.) .)a)-.)-/&Te.) .)a)-.)-/& : O- E- ;: O- E- ;!!

XX**!! ??[[ E-E- O- ? (.e+8e 3+e=e'/-e. -' -O- ? (.e+8e 3+e=e'/-e. -' -)*)*+ + )*)*/lm'/lm'

E- ? expe/)e 3+e=e'/-e. -' -E- ? expe/)e 3+e=e'/-e. -' - )*)*+ + )*)*/lm'/lm'

E


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E MODERATE HIH WORK-SHIFTWORK-SHIFT MORNIN :I; %0 %5 50MORNIN :I; %0 %5 50 AFTERNOON:II; #0 55 #0AFTERNOON:II; #0 55 #0

NIHT:III; %0 "0 !5NIHT:III; %0 "0 !5 Ba.e ' )*e a)a /lle/)e, >*a) -. 4+ /'/l.-'


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$H% SUARE: INDEPENDEN$% TEST$H% SUARE: INDEPENDEN$% TEST

DISTRIBUTION OF DATA COLLECTED BY UNILEVERDISTRIBUTION OF DATA COLLECTED BY UNILEVERINDONESIA >AS RECORDED AS FOLLO>INDONESIA >AS RECORDED AS FOLLO>&&

Cl+ 3 (a)* .ap& P-' >*-)e YellCl+ 3 (a)* .ap& P-' >*-)e Yell e'e+& Ma' 10 10 !0e'e+& Ma' 10 10 !0 >ma' !5 !0 5>ma' !5 !0 5

>*a) -. 4+ /'/l.-'< : U.eAlp*a ? 5 ;>*a) -. 4+ /'/l.-'< : U.eAlp*a ? 5 ;

Exe+/-.e.& /*e/ 4+ ( p & ##1##!##"2Exe+/-.e.& /*e/ 4+ ( p & ##1##!##"2

ANAL%SIS of VARIAN$EANAL%SIS of VARIAN$E


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ANAL%SIS of VARIAN$EANAL%SIS of VARIAN$E

T*-. me)* /a' (e .e ) )e.) )*e -33e+e'/eT*-. me)* /a' (e .e ) )e.) )*e -33e+e'/eam'9 ppla)-' mea'. : )*e 'm(e+ 3am'9 ppla)-' mea'. : )*e 'm(e+ 3.pe/-3-/ .ample -. m+e )*a' ) + \ !2.pe/-3-/ .ample -. m+e )*a' ) + \ !2

T*e .)ep. 3 )e.)-'9 )*e *4p)*e.-.2T*e .)ep. 3 )e.)-'9 )*e *4p)*e.-.2 12 Cal/la)e )*e 8a+-a'/e -)*-' .ample. :12 Cal/la)e )*e 8a+-a'/e -)*-' .ample. : !!55;2;2 !2 Cal/la)e 8a+-a'/e (e)ee' + am'9 )*e!2 Cal/la)e 8a+-a'/e (e)ee' + am'9 )*e

.ample. :.ample. :!!((;2;2 "2 Cal/la)e F )a(le2"2 Cal/la)e F )a(le2 %2 Cal/la)e F .)a)-.)-/2%2 Cal/la)e F .)a)-.)-/2


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!.!. ANAL%SIS OF VARIAN$EANAL%SIS OF VARIAN$E

FERTILIER: A B $ DFERTILIER: A B $ DSAMPLESAMPLE

(( (& 8 (# 8 (( 8 ! 8(& 8 (# 8 (( 8 ! 8

## (# (( (& (&(# (( (& (&

( (& ! '( (& ! '** (( (& (& '(( (& (& '

)) (* (# (& (&(* (# (& (&

$,9 3o0 co9c05 74,7 745 ,5r,5 Cro0c773 of 74o5$,9 3o0 co9c05 74,7 745 ,5r,5 Cro0c773 of 74o5

f5r75r ,r5 9fc,973 ff5r597 @ ,C4, ? ) .f5r75r ,r5 9fc,973 ff5r597 @ ,C4, ? ) .

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20140905 Probability Sam