5169e59a-2703-43ae-acf0-e03bcb5eacd3

5169e59a-2703-43ae-acf0-e03bcb5eacd3 - C h a p t e r 8 C h...

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Unformatted text preview: C h a p t e r 8 C h a p t e r 8 C o n f i d e n c e I n t e r v a l s A i m s I n t h i s c h a p t e r w e d e a l w i t h : C o n s t r u c t i n g c o n f i d e n c e i n t e r v a l s b y h a n d T h e l e v e l o f c o n f i d e n c e T h e w i d t h o f t h e c o n f i d e n c e i n t e r v a l S a m p l e s i z e i s s u e s T h e m a r g i n o f e r r o r I n t e r p r e t i n g c o n f i d e n c e i n t e r v a l s B y t h e e n d o f t h i s c h a p t e r y o u s h o u l d : ¡ b e a b l e t o s t a t e t h e 4 p a r a m e t e r s t h a t w e b u i l d c o n f i d e n c e i n t e r v a l s f o r i n t h i s c h a p t e r ¡ k n o w h o w t o c o n s t r u c t a c o n f i d e n c e i n t e r v a l b y h a n d f o r e a c h o f t h e s e 4 p a r a m e t e r s ¡ b e a b l e t o i n t e r p r e t a c o n f i d e n c e i n t e r v a l i n p l a i n E n g l i s h ¡ u n d e r s t a n d t h e n a t u r e o f c o n f i d e n c e l e v e l s ¡ w h a t i s m e a n t b y t h e l e v e l o f c o n f i d e n c e ¡ w h a t a f f e c t s t h e w i d t h o f a c o n f i d e n c e i n t e r v a l ¡ w h a t i s m e a n t b y t h e m a r g i n o f e r r o r P a g e 1 S i n g l e M e a n , μ P a r t T i m e W o r k I W h a t i s t h e a v e r a g e n u m b e r o f h o u r s w o r k e d p e r w e e k b y a l l t h o s e S t a g e 1 S t a t i s t i c s s t u d e n t s w h o h a v e a p a r t t i m e j o b t h r o u g h t h e s e m e s t e r ? H o u r s w o r k e d p e r w e e k : 2 5 1 2 1 2 1 3 1 2 1 3 4 8 6 1 5 1 2 ( 1 2 s t u d e n t s ) ( S o u r c e : S t a g e 1 S t a t i s t i c s o n l i n e s u r v e y ) M e t h o d : U s e t h e s a m p l e d a t a , t o p r o d u c e a r a n g e o f b e l i e v a b l e v a l u e s f o r μ , i . e . , a n i n t e r v a l e s t i m a t e . ¡ A s s u m e t h e 1 2 o b s e r v a t i o n s f o r m a r a n d o m s a m p l e f r o m a p o p u l a t i o n w i t h m e a n μ . ¡ U s e t h e s a m p l e m e a n , x = 1 2 . 5 h o u r s a s a ( p o i n t ) e s t i m a t e f o r μ . ¡ T h i s e s t i m a t e i s b a s e d u p o n a p a r t i c u l a r s a m p l e ; a n o t h e r s a m p l e w i t h 1 2 d i f f e r e n t s t u d e n t s w o u l d g i v e a d i f f e r e n t v a l u e f o r t h e e s t i m a t e , i . e . , t h i s e s t i m a t e v a l u e v a r i e s f r o m s a m p l e t o s a m p l e . ¡ W e s a y ‘ t h i s e s t i m a t e i s s u b j e c t t o s a m p l i n g v a r i a b i l i t y ’ . ¡ P l a c e a t- s t a n d a r d- e r r o r i n t e r v a l a r o u n d t h e e s t i m a t e t o a l l o w f o r t h e u n c e r t a i n t y d u e t o t h e s a m p l i n g v a r i a b i l i t y : e s t i m a t e ± t × s e ( e s t i m a t e ) ¡ S e t t h i s m e t h o d ’ s s u c c e s s r a t e a t 9 5 % ( i . e . , v e r y l i k e l y t o w o r k ) ¡ A s s u m e t h e d a t a c o m e f r o m a N o r m a l d i s t r i b u t i o n , i . e , , t h e p o p u l a t i o n h a s a N o r m a l d i s t r i b u t...
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This note was uploaded on 08/19/2011 for the course INTBUS 211 taught by Professor Daniel during the Winter '10 term at Auckland University of Technology.

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5169e59a-2703-43ae-acf0-e03bcb5eacd3 - C h a p t e r 8 C h...

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