An employee of a small software company in Minneapolis bikes towork during the summer months. He can travel to work using one ofthree routes and wonders whether the average commute times (inminutes) differ between the three routes. He obtains the followingdata after traveling each route for one week.
| | | | | |
| Route 1 | 32 | 35 | 33 | 28 | 35 |
| Route 2 | 22 | 24 | 25 | 24 | 22 |
| Route 3 | 29 | 30 | 20 | 20 | 27 |
|
a-1. Construct an ANOVA table. (Round\"Sum Sq\" to 1 decimal place, \"Mean Sq\" and\"F value\" to 2, and round the \"p-value\" to 4decimal places.)
ANOVA
| Source of Variation | Df | Sum Sq | Mean Sq | F value | Pr(>F) |
|---|
| Route | | | | | |
| Residuals | | | | | |
a-2. At the 5% significance level, do theaverage commute times differ significantly between the threeroutes. Assume that commute times are normally distributed.
Yes, since the p-value is less than significancelevel.
Yes, since the p-value is not less than significancelevel.
No, since the p-value is less than significancelevel.
No, since the p-value is not less than significancelevel.
b. Use Tukey’s HSD method at the 5%significance level to determine which routes' average times differ.(Round difference to 1 decimal place, confidence intervalbounds to 2 decimal places, and p-values to 3.)
| Population Mean Difference | diff | lwr | upr | p adj | do the average times differ? |
|---|
| Route 2 - Route 1 | | | | | |
| Route 3 - Route 1 | | | | | |
| Route 3 - Route 2 | | | | | |
