31. FILE (Use Excel) A variety o f p a ck a g in g solut ion s exis t for product s th a t mu s t b e kept within a spe cif ic temp e r a tu r e range. Cold chain distribution is particularly useful in th e fo o d and pharmaceut ical indus tries . A p a ck a g in g c om p a n y is trying o u t a n ew p a ck a g in g material th a t migh t r ed uc e th e variation o f temp e r a tu r e s in th e box. It is b e l ie v ed that th e temp e r a tu r e in th e bo x fo l lows a normal dis tribution with b o th p a ck a g in g materials. Inspectors r andomly s e le c t 16 b o x e s o f n ew and old p a cka g e s , 2 4 hours after th e y are s e a le d for sh ipmen t , a nd report th e temp e r a tu r e s in d e g r e e s Celsius. We a s sum e th a t th e tw o s amp le s are drawn in d ep en d e n t ly from normally dis tributed p op ula t ion s . A por t ion o f th e data is s h ow n be low; th e c om p l e t e data, labe led P a c k a g in g , are available o n th e te x t web s i t e .

N e w P a c k a g e O ld P a c k a g e 3.98 5.79 4.99 6.42

⋮ ⋮

4.95 5.95

a. State th e appropriate h y p o th e s e s to t e s t w h e th e r or n o t th e n ew pa cka g in g material r ed uc e s th e variation o f t emp e r a tu r e s in th e box.

b. Use Excel's F.TEST fu n c t ion t o c a lculate th e p -value.

c. Make a c on c lu s io n at th e 5% s ignif ican ce level.