Question

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	33	35	35	35	30
Route 2	29	22	24	27	26
Route 3	30	20	30	25	24

Data
Route 1	33	35	35	35	30
Route 2	29	22	24	27	26
Route 3	30	20	30	25	24

a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS", "p-value" to 4 decimal places and "F" to 3 decimal places.)

ANOVA
Source of Variation   SS   df   MS   F   p-value
Between Groups                  
Within Groups                  

a-2. At the 1% significance level, do the average commute times differ between the three routes. Assume that commute times are normally distributed.

• Yes since the p-value is less than significance level.
• No  since the p-value is less than significance level.
• No  since the p-value is not less than significance level.
• Yes  since the p-value is not less than significance level.

b. Use Tukey’s HSD method at the 1% significance level to determine which routes' average times differ. (You may find it useful to reference the q table). (If the exact value for n_T − c is not found in the table, use the average of corresponding upper & lower studentized range values. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Population Mean Difference   Confidence Interval   Do the average times differ?
μRoute 1 − μRoute 2 [       ,       ]  
μRoute 1 − μRoute 3 [       ,       ]  
μRoute 2 − μRoute 3 [       ,       ]  

Answer 1