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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

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Answer:

16

Step-by-step explanation:

Remember that the general formula for SSTR is

[tex]SSTR = n_1(\bar{x_1}-\bar{x})+...+n_k(\bar{x_k}-\bar{x})[/tex]

For this problem

[tex]\bar{x} = 8[/tex]

[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex]

then

[tex]n_1(\bar{x_1}-\bar{x})+...+n_k(\bar{x_k}-\bar{x}) = 32[/tex]

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

[tex]MSTR = \frac{SSTR}{t-1}[/tex]

where [tex]t[/tex] is the number of treatments, for this case the number of treatments is 3 so [tex]t = 3[/tex] and

[tex]MSTR = \frac{32}{3-2} = \frac{32}{2} = 16[/tex]

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