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 find the mean square for treatments, we need to first calculate the sum of squares for treatments (SSTR) and degrees of freedom for treatments (dfT).

We can calculate SSTR by finding the sum of squares of the differences between each group mean and the overall mean. The overall mean is the mean of all the observations across all three groups.

Overall Mean: (17+12+14+15+18+20+22+27+25+24+28+26+29+31+30)/15 = 21

SSTR = [(17-21)^2 + (12-21)^2 + (14-21)^2 + (15-21)^2 + (18-21)^2 + (20-21)^2 + (22-21)^2 + (27-21)^2 + (25-21)^2 + (24-21)^2 + (28-21)^2 + (26-21)^2 + (29-21)^2 + (31-21)^2 + (30-21)^2]

SSTR = 424

dfT = number of groups - 1 = 3 - 1 = 2

Mean Square for Treatments = MSTR = SSTR/dfT = 424/2 = 212/1 = 16

Therefore, the answer is C) 16.0.