AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. The following data represent the age of a random sample of trucks, cars, and vans. The mean square for treatments MSTR for these observations is ________.
A) 2.0
B) 4.7
C) 16.0
D) 12.5

Question

AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. The following data represent the age of a random sample of trucks, cars, and vans.  The mean square for treatments MSTR for these observations is ________.
A) 2.0 
B) 4.7 
C) 16.0 
D) 12.5

Quizplus · Accepted Answer

To calculate the mean square for treatments, first calculate the sum of squares for treatments (SSTR) and divide it by the degrees of freedom for treatments (k-1). Using the data provided in the link, we get:
- Trucks: (8-8.2)^2 + (5-8.2)^2 + (10-8.2)^2 + (9-8.2)^2 + (7-8.2)^2 = 10.8
- Cars: (3-4.4)^2 + (4-4.4)^2 + (5-4.4)^2 + (2-4.4)^2 + (6-4.4)^2 = 10.4
- Vans: (6-5.6)^2 + (8-5.6)^2 + (7-5.6)^2 + (5-5.6)^2 + (6-5.6)^2 = 6.4
SSTR = 10.8 + 10.4 + 6.4 = 27.6
k-1 = 3-1 = 2
MSTR = SSTR/(k-1) = 27.6/2 = 13.8
Therefore, the closest option is C) 16.0.