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Page 1: SIMULATION TOPIC 6

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Page 2: SIMULATION TOPIC 6

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Page 3: SIMULATION TOPIC 6

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Page 4: SIMULATION TOPIC 6

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Page 5: SIMULATION TOPIC 6

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Page 6: SIMULATION TOPIC 6

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Page 7: SIMULATION TOPIC 6

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N e x t t w o p a g e s

C hi -s qu a r e t e s t (t e x t b o o k s e c t i o n 5 . 8 . 3) :

c h i -s qu a r e , K o l m o g o r o v - Sm i r n o v , o r A n de r s o n - D a r l i n g

Pe r f o r m a g o o d n e s s -o f : f i t h y p o t h e s i s t e s t

M a n u a l f 1t t i n g :

F i t + G o o d n e s s o f F i t

F i t j A u t o : : F i t

P r o M o d e > s S t a t : : F i t u t i l i t y

(a) A u t o m a t i c f i t t i n g :

I n v o l v e s" f i t t i n g

"

a d i s t r i b u t i o n t o t h e d a t a

(I I I ) T he o r e t i c a l d i - (e . g . Tr i a n g u l a r , e xp

o n , n o r m a l , e t c . )in t e r v a l ; t h e r e a l # s w i t h i n a g i v e n i n t e r v a l a r e a s s u m e d t o b e e q u a l l y l i k e l y t o o c c m .

T h e p r o b a b i l i t y d i s t r i b u t i o n a s s i g n s 3 / 2 0 , 8 /20 , 5/20 , 4 / 2 0 p

r o b a b i l i t y t o e a c h

EX . 2 0 o b s e r v a t i o n s r e c o r d e d a n d h i s t o g r a m h a s 4 i n t e r v a l s w l f r e q u e n c i e s 3 , 8 , 5 , 4 .

(I I ) C o n t i n u o u s e m p i r i c a l l i - o n B a s e d o n h i s t o g r a m f r o m o b s e r v e d d a t a .

EX . I f 50 o b s e r v a t i o n s r e c o r d e d , a s s i gn a 2 % p r o b a b i l i t y t o e a c h o b s e r v e d v a l u e .

(I ) D i mR o i r i c a l d i s t r i b u t i o n . T h e e x a c t v a l u e s o f t h e o b s e r v a t i o n s a r e u s e d .

da t a i n y o u r m o d e l . T h r e e o p t i o n s :

(D ) D o t h i s o n l y a f t e r y o u r d a t a p a s s e s s t e p s B a n d c . Se l e c t a p r o b a b i l i t y d i s t r i b u t i o n t o r e p r e s e n t t h i s

(c ) T e s t i f d a t a i s i n d e p e n d e n t , I . e . I f o b s e r v a t i o n s n o t r e l a t e d t o e a c h o t h e r ( t w o r u n s t e s t s & s c a t t e 中 l o t )

(B ) Ju d g e i f d a t a a p p e a r s t o b e i dent i ca1. m§st r m I . e . I f o b s e r v a t i o n s c o m e f r o m s a m e d i s t r i b u t i o n

G o t o I n p u t + O p t i o n s t o c h a n g e # o f i n t e r v a l s

I n p u t + I n p u t G r a p h

T y p e y o u r d a t a i n t o t h e d a t a t a b l e

C l i c k o n S t a t : : F i t i n P r o M o d e l s h o r t c u t p a n e l

St a r t P r o M o d e l

Pr oBode>s S t a t : : t m u t i l i t y l l m æ 5 i n t e x t b H & R 1

[de m o ]

T o o l s + D a t a A n a l y s i s + H i s t o g r a m

T o o l s j A d d l n s + A n a l y s i s T o o l p a k

M - E x c e l 2 0 0 3

So f t w a r e c a n c o n s t r u c t h i s t o g r a m s a u t o m a t i c a l l y

H o w m a n y i n t e r v a l s G o o d s t a r t i s (2n )" 3

( n - # o b s e r v a t i o n s ) . T he n a d j u s t i f d e s i r e d .

Pl o t f r e q u e n c y v e r t i c a l l y

D e t e r m i n e # o f o c c u r r e n c e s (f r e q u e n c y ) o f r a w d a t a i n e a c h i n t e r v a t

D i v i d e d a t a r a n g e i n t o i n t e r v a l s o f e q u a l l e n g t h

H o w t o c o n s t r u c t :

U s e f u l f o r i dent i ng t h e s h a p e o f a d i s t D b u t i o n

H i s t o g r a m s :

(A ) M a k e h i s t o g r a m f r o m t h e r a w d a t a

R a w d a t a l o o k s l i k e t h i s : 2 . 7 13 , 3 . 9 2 8 , 3 . 3 5 5 , . . ’

A n a l y z i n g n u m e r i c a l d a t a a n d i n c o r p o r a t i n g i t i n t o s i m - mr a l

Sy l l a b u s T o p i c 6 : D a t a c o l l e c t i o n a n d a n a l y s i s ( t e x t b o o k C h a p t e r 5 )

Sp r i n g 2 0 1 5

I n d u s t r i a l & M a n u f a c t u f i n g E n g i n e e r i n g 4 7 5 : S i m u l a t i o n M e t h o d o l o g y

Page 8: SIMULATION TOPIC 6

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Page 11: SIMULATION TOPIC 6

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w i t h n - 1 d e g r e e s o f f r e e d o m e x c e e d s t h e v a l u e t . 1 , 0 / 2 •

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Page 12: SIMULATION TOPIC 6

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T h e a b o v e p r o c e d u r e i s c a l l e d t h e W e l c h c o n f +d e n c e i n t e r v a l m e t h o d .

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m e a n f o r o n e p o p u l a t i o n i s d i f f e r e n t t h a n t h e t r u e (u n k n o w n ) m e a n f o r t h e o t h e r p o p u l a t i o n .

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