A researcher with the 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 times (in minutes) to work. Note that the grand mean is 36.625. 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

A researcher with the 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 times (in minutes) to work. Note that the grand mean is 36.625.  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

The sum of squares due to treatments can be calculated using the formula SST = Σ(ni*(Ybari-Ybar)^2), where ni is the sample size for each city, Ybari is the mean commute time for each city, and Ybar is the grand mean. Plugging in the values, we get SST = 6*(29.5-36.625)^2 + 6*(38.33-36.625)^2 + 6*(42.67-36.625)^2 + 6*(44.33-36.625)^2 = 13,281.79. Therefore, the correct answer is B.

A Researcher with the Ministry of Transportation Is Commissioned to Study