26. A firm h as ju s t d e v e l o p e d a n e w c o s t -r e d u c in g t e c h n o l o g y for producing a certain rep lacem en t part for autom obiles. Since a replacem ent part m ust be produced within close specifications in order for it to b e a c c e p ta b le to cu stom ers, the n ew technology's specifications m ust not deviate drastically from th e o ld er version. S u p p o s e t h e s a m p le variance for 15 parts p r o d u ce d u sing th e older version is s21 = 0 .35, w h ile t h e s a m p le va r ia n c e for 15 parts p r o d u ce d using th e n e w te c h n o lo g y is s22 = 0.48. A ssum e that th e tw o s a m p le s are d raw n in d e p e n d e n t ly from norm ally distribu ted populations.

a. D evelop th e h y p o th eses to test w h eth er th e population variances differ.

b. Calculate th e appropriate te s t statistic.

c. Using th e critical v a lu e approach, d e t e rmin e th e de c i s ion rule at th e 5% s igni f icance level.

d. Can you c o n c lu d e th a t th e variances are dif ferent? Given th a t all o th e r criteria are satisfied, sh ou ld th e c omp a n y a d o p t th e n ew te ch n o lo g y ?