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3-3 D is c u ssio n: C onfid en ce I n te rv als a n d

H yp oth esis T e stin g

Availa b le o n M ar 1 2, 2 022 1 1:5 9 P M . S u b m is sio n r e str ic te d b efo re a v aila b ili t y s ta rts . M ust p o st f ir s t.

M AT-2 43-J 4 48 8 A ppli e d S ta tis tic s f o r S T EM 2 2EW 4

Dis c u ssio ns L is t V ie w T o pic S ett in gs H elp

S u b sc rib e

U se t h e li n k in t h e J u pyte r N ote b o ok a ctiv it y t o a cce ss y o ur P yth o n s c rip t. O nce

y o u h av e m ad e y o ur c a lc u la tio ns, c o m ple te t h is d is c u ssio n. T he s c rip t w ill o utp ut

an sw ers t o t h e q uestio ns g iv e n b elo w . Y o u m ust a tta ch y o ur P yth o n s c rip t o utp ut

as a n H TM L f ile a n d r e sp o nd t o t h e q uestio ns b elo w .

In t h is d is c u ssio n, y o u w ill a p ply t h e s ta tis tic a l c o nce p ts a n d t e ch niq ues c o ve re d in

t h is w eek's r e ad in g t o c a lc u la te a c o nfid en ce in te rv al a n d p erfo rm h yp oth esis

t e stin g f o r a m an ufa ctu rin g p ro ce ss.

T he m an ufa ctu rin g p ro ce ss a t a f a cto ry p ro duce s b all b earin gs t h at a re s o ld t o

a u to m otiv e m an ufa ctu re rs . T he f a cto ry w an ts t o e stim ate t h e a v e ra g e d ia m ete r o f

a b all b earin g t h at is in d em an d t o e n su re t h at it is m an ufa ctu re d w it h in t h e

sp ecif ic a tio ns. S u p po se t h ey p la n t o c o lle ct a s a m ple o f 5 0 b all b earin gs a n d

m easu re t h eir d ia m ete rs t o c o nstr u ct a 9 0% a n d 9 9% c o nfid en ce in te rv al f o r t h e

av e ra g e d ia m ete r o f b all b earin gs p ro duce d f ro m t h is m an ufa ctu rin g p ro ce ss. The s a m ple o f s iz e 5 0 w as g e n era te d u sin g P yth o n's n um py m odule . T his d ata s e t

w ill b e u n iq ue t o y o u, a n d t h ere fo re y o ur a n sw ers w ill b e u n iq ue a s w ell. R un S te p

1 in t h e P yth o n s c rip t t o g e n era te y o ur u n iq ue s a m ple d ata . C heck t o m ake s u re

y o ur s a m ple d ata is s h o w n in y o ur a tta ch m en t.

In y o ur in it ia l p o st, a d dre ss t h e f o llo w in g it e m s. B e s u re t o a n sw er t h e q uestio ns

ab o ut b oth c o nfid en ce in te rv als a n d h yp oth esis t e stin g.

1 . I n t h e P yth o n s c rip t, y o u c a lc u la te d t h e s a m ple d ata t o c o nstr u ct a 9 0% a n d

9 9% c o nfid en ce in te rv al f o r t h e a v e ra g e d ia m ete r o f b all b earin gs p ro duce d

fro m t h is m an ufa ctu rin g p ro ce ss. T hese c o nfid en ce in te rv als w ere c re ate d

u sin g t h e N orm al d is tr ib utio n b ase d o n t h e a ssu m ptio n t h at t h e p o pula tio n

sta n d ard d evia tio n is k n o w n a n d t h e s a m ple s iz e is s u ffic ie n tly la rg e . R ep o rt

th ese c o nfid en ce in te rv als r o un d ed t o t w o d ecim al p la ce s. S ee S te p 2 in t h e

P yth o n s c rip t.

2 . I n te rp re t b oth c o nfid en ce in te rv als . M ake s u re t o b e d eta ile d a n d p re cis e in

y o ur in te rp re ta tio n.

It h as b een c la im ed f ro m p re vio us s tu d ie s t h at t h e a v e ra g e d ia m ete r o f b all

b earin gs f ro m t h is m an ufa ctu rin g p ro ce ss is 2 .3 0 c m . B ase d o n t h e s a m ple o f 5 0

th at y o u c o lle cte d , is t h ere e vid en ce t o s u gge st t h at t h e a v e ra g e d ia m ete r is

g re ate r t h an 2 .3 0 c m ? P erfo rm a h yp oth esis t e st f o r t h e p o pula tio n m ean a t a lp ha

= 0 .0 1.

In y o ur in it ia l p o st, a d dre ss t h e f o llo w in g it e m s:

1 . D efin e t h e n ull a n d a lt e rn ativ e h yp oth esis f o r t h is t e st in m ath em atic a l

te rm s a n d in w ord s. Rub ric s

D is c u ssio n R ub ric : U nd erg ra d uate

S ta rt a N ew T hre ad

2 . R ep o rt t h e le ve l o f s ig n if ic a n ce .

3 . I n clu d e t h e t e st s ta tis tic a n d t h e P -v alu e. S ee S te p 3 in t h e P yth o n s c rip t.

(N ote t h at P yth o n m eth o ds r e tu rn t w o t a ile d P -v alu es. Y o u m ust r e p o rt t h e

co rre ct P -v alu e b ase d o n t h e a lt e rn ativ e h yp oth esis .)

4 . P ro vid e y o ur c o nclu sio n a n d in te rp re ta tio n o f t h e r e su lt s . S h o uld t h e n ull

h yp oth esis b e r e je cte d ? W hy o r w hy n ot?

In y o ur f o llo w -u p p o sts t o o th er s tu d en ts , r e vie w y o ur p eers ' c a lc u la tio ns a n d

p ro vid e s o m e a n aly sis a n d in te rp re ta tio n:

1 . H ow d o t h eir c o nfid en ce in te rv als c o m pare w it h y o urs ?

2 . I f t h e p o pula tio n s ta n d ard d evia tio n is u n kn o w n a n d t h e s a m ple s iz e is n ot

su ff ic ie n tly la rg e , w ould y o u s till u se t h e N orm al d is tr ib utio n t o c a lc u la te

t h ese c o nfid en ce in te rv als , o r w ould y o u c h o ose a n oth er d is tr ib utio n? I f

t h e la tte r, w hic h d is tr ib utio n w ould y o u c h o ose ?

R em em ber t o a tta ch y o ur P yth o n o utp ut a n d r e sp o nd t o a ll q uestio ns in y o ur

in it ia l a n d f o llo w -u p p o sts . B e s u re t o c le arly c o m mun ic a te y o ur id eas u sin g

ap pro pria te t e rm in o lo gy. F in ally , b e s u re t o r e vie w t h e D is c u ssio n R ub ric t o

u n d ers ta n d h o w y o u w ill b e g ra d ed o n t h is a ssig n m en t. Filt e r b y:

So rt b y:

M ost R ece n t A ctiv it y

Y o u m ust s ta rt a t h re ad b efo re y o u c a n r e ad a n d r e p ly t o o th er t h re ad s

All T hre ad s