# Southway Shuttle provides a shuttle service from Lincoln Heights

March 14, 2016

Question
Southway Shuttle provides a shuttle service from Lincoln Heights to the airport. There are three main routes that the shuttle can take: Highway 40, Tall Pine Road, and Route 81. Southway is looking to determine if any of the routes tend to be faster than others and if time of day of travel–morning or evening–makes a difference.

For each route, Southway chose morning trips at random and evening trips at random and recorded their durations (the time it took for the trip, in minutes). Then Southway computed the mean trip duration for each of the six groups. These mean trip durations are displayed in the graph below.

After checking that the assumptions for the test were satisfied, Southway performed a two-way ANOVA test. (The dependent variable was trip duration, and the factors were time of day and route.) The partially filled ANOVA table is shown below. Complete the table, and then answer the questions after the table. Do not round any values in the table except the F statistic values, which you should round to at least three decimal places.

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