Young affluent U.S. professionals are creating a growing demand for exotic pets.
ID: 3206253 • Letter: Y
Question
Young affluent U.S. professionals are creating a growing demand for exotic pets.The most popular pets are the Shiba Inu dog breed, Rottweilers, Persian cats,
and Maine coons. Prices for these pets vary and depend on supply and demand. A breeder of exotic pets wants to know whether these four pets fetch the
same average prices, whether prices for these exotic pets are higher in some geographic areas than in others, and whether there are any interactions-one or more of the four pets being more favored in one location than in others. Prices for l0 of each of these pets at four randomly chosen locations around the country are recorded and analysed. The results are SS(pet)=22,245, SS(location)=34,551, SS(interaction)=31,778 and SSE= 554,398. Are there any pet main effects? Are there any location main effects?Are there any pet-location interactions? Explain your findings.
Explanation / Answer
The degrees of freedom for main factor, pets is: row-1=4-1=3.
The degrees of freedom for main factor, location is: column-1=4-1=3.
The degrees of freedom for interaction is: (row-1)(column-1)=3*3=9
The degrees of freedom for Error is: number of samples- (row*column)=(10*4*4)-16=144
MS(Pet)=SS(Pet)/df(Pet)=22,245/3=7415
MS(Location)=SS(Location)/df(Location)=34551/3=11517
MS(Interaction)=SS(Interaction)/df(Interaction)=31778/9=3530.89
MS(Error)=SSE/df(Error)=554398/144=3849.986
F(Pet)=MS(Pet)/MS(Error)=7415/3849.986=1.93, p value for df(3, 144)=0.1273
F(Location)=MS(Location)/MS(Error)=11517/3849.986=2.99, p value for df(3, 144)=0.0330
F(Interaction)=MS(Interaction)/MS(Error)=3530.89/3849.986=0.92, p value for df(9, 144)=0.5097
Conclude any factor to have significant effect, if the corresponding p value is less than 0.05. Therefore, except main factor location, no other factors are supposed to have significant effect.
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