Question

AutoTrader 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. Trucks Cars Vans 12 8 3 8 7 7 9 10 6 11 7 8 The mean square for treatments MSTR for these observations is ________. Multiple Choice 2.0 4.7 16.0 12.5

Answer 1

Answer:

16

Step-by-step explanation:

Remember that the general formula for SSTR is

$SSTR = n_1(\bar{x_1}-\bar{x})+...+n_k(\bar{x_k}-\bar{x})$

For this problem

$\bar{x} = 8$

$n_1 = n_2 = n_3 = n_4 = 4$

then

$n_1(\bar{x_1}-\bar{x})+...+n_k(\bar{x_k}-\bar{x}) = 32$

so once you have the SSTR then the MSTR is given by the following formula

$MSTR = \frac{SSTR}{t-1}$

where $t$ is the number of treatments, for this case the number of treatments is 3 so $t = 3$ and

$MSTR = \frac{32}{3-2} = \frac{32}{2} = 16$