An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in minutes) differ between the three routes. He obtains the following data after traveling each route for one week.

Route 1 32 27 35 33 32
Route 2 21 28 20 22 26
Route 3 28 24 24 20 20

The following one-way ANOVA results were obtained for α = 0.01:

ANOVA
Source of Variation SS df MS F p-value F crit
Between Groups 240.93 2 120.47 11.400 0.0017 6.93
Within Groups 126.80 12 10.57
Total 367.73

a. At the 1% significance level do the average commute times differ between the three routes.

1. Yes, since the p-value is less than α.
2. Yes, since the p-value is not less than α.
3. No, since the p-value is less than α.
4. No, since the p-value is not less than α.

b. Use Tukey’s HSD test at the 1% significance level to determine which routes' average times differ. Use Table 5. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)