13. The m a n a g e r o f a su p e rma r k e t w o u ld like th e v a r ian c e o f th e w a i t in g t im e s o f th e c u s t om e r s n o t t o e x c e e d 3 m in u t e s - sq u a r e d . S h e w o u ld a d d a n ew c a sh r eg i s te r if th e v a r ian c e e x c e e d s thi s th r e sh o ld . S h e regularly ch e ck s t h e w a i t in g t im e s o f th e c u s t om e r s t o e n s u r e th a t its v a r ian c e d o e s n o t rise a b o v e t h e a l low e d lev e l . In a r e c e n t r a n d om s am p l e o f 2 8 c u s t om e r w a i t in g t im e s , s h e c om p u t e s th e s am p l e v a r ian c e as 4 .2 m in u t e s -

s q u a r ed . S h e b e l i e v e s th a t th e w a i t in g t im e s are no rma l ly d i s tr ib u ted .

a. State th e null and th e alternat ive h y p o th e s e s to te s t if th e th re shold has b e e n cros sed.

b. Use th e p -value approach to c o n d u c t th e te s t at

α = 0.05.

c. Repeat th e analys is wi th th e critical v a lue approach.

d. What sh ou ld th e ma n a g e r do?