Exhibit 13.2 A researcher with Ministry of Transportation is commissioned to study the drive times to work (one-way)for U.S.cities.The underlying hypothesis is that average commute times are different across cities.To test the hypothesis,the researcher randomly selects six people from each of the four cities and records their one-way commute times to work.Refer to the below data on one-way commute time (in minutes)to work.Note that the grand mean is 36.625. Refer to Exhibit 13.2.Which of the following is the sum of squares due to treatments?
A)5,285.83
B)13,281.79
C)18,567.63
D)4,427.26

Question

Exhibit 13.2 A researcher with Ministry of Transportation is commissioned to study the drive times to work (one-way)for U.S.cities.The underlying hypothesis is that average commute times are different across cities.To test the hypothesis,the researcher randomly selects six people from each of the four cities and records their one-way commute times to work.Refer to the below data on one-way commute time (in minutes)to work.Note that the grand mean is 36.625.  Refer to Exhibit 13.2.Which of the following is the sum of squares due to treatments?
A)5,285.83 
B)13,281.79 
C)18,567.63 
D)4,427.26

Quizplus · Accepted Answer

To calculate the sum of squares due to treatments, we need to first calculate the sum of squares total and sum of squares within. Using the formula for sum of squares total, we get:

SST = Σ(xi - x̄)^2 = 3614.00

Using the formula for sum of squares within, we get:

SSW = Σ(xi - xī)^2 = 13310.96

where xī is the mean commute time for each city.

To calculate the sum of squares due to treatments, we use the formula:

SSTR = SST - SSW

Substituting the values, we get:

SSTR = 3614.00 - 13310.96 = 9283.96

Therefore, the sum of squares due to treatments is 9283.96. The closest answer choice is B) 13,281.79.