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

16

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 = (SSTR)/(t-1)`

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

`MSTR = (32)/(3-2) = (32)/(2) = 16`