The m a n a g er o f a su perm ark et w o u ld like th e variance o f t h e w a i t i n g t i m e s o f t h e c u s t o m e r s n o t t o e x c e e d 3 m in u tes-sq u ared . Sh e w o u ld ad d a n e w cash register if th e v a rian ce e x c e e d s this th re sh o ld . S h e regularly ch eck s th e w a itin g tim es o f th e c u sto m e r s to en su re th at its v a r ia n c e d o e s n o t rise a b o v e t h e a l l o w e d le v e l. In a recent random sam p le of 28 cu stom er w aiting tim es, she c o m p u te s th e sa m p le variance as 4.2 m in utessquared. She believes that th e w aiting tim es are norm ally distributed.

a. State th e null and th e alternative h y p o th eses to test if the threshold has been crossed.

b. Use th e p -value approach to c o n d u ct th e test at

α = 0.05.

c. R epeat th e analysis w ith th e critical v alu e approach.

d. What should th e m anager do?