An em p lo y e e o f a small softw are com p an y in M inneap olis bikes to w o rk du ring th e s u m m e r m onths. He can travel to w o rk using one o f three routes and w onders w h e th e r th e average c o m m u te tim es (in m inutes) differ b etw e e n th e three routes. He obtains th e follow ing data after traveling each route for on e w eek.

Route 1 29 30 33 30 32 Route 2 27 32 28 30 29 Route 3 25 27 24 29 26 T h e fo llo w in g o n e -w a y A N O V A results w e re o b ta in e d fo r α = 0.01:

ANOVA Source of Variation SS df MS F p-value F crit Between Groups 54.53 2 27.27 8.099 0.0059 6.93 Within Groups 40.40 12 3.37 Total 94.93 14

a. D e te rm in e a t th e 1 % sign ificance level w h e th e r th e average c o m m u te tim es differ b etw een th e three routes.

b. If differences exist, use Tukey's H S D test at t h e 1 %

significance level to d e te rm in e w h ic h ro u te s ' ave ra g e tim es differ.