The city of Tucson Arizona employs people to assess the valu

The city of Tucson, Arizona, employs people to assess the value of homes for the purpose of establishing real estate tax. The city manager sends each assessor to the same five homes and then compares the results. The information is given below, in thousands of dollars. Can we conclude that there is a difference in the assessors, at a = 0.05? Is there a difference in the treatment means, at a = .05? The computed F value is Is there a difference in the block means, at a = .05? The computed F is

Solution

The ANOVA table is given by

Two-way ANOVA: Response versus block factor, treatment factor

Source DF SS MS F P
block factor 4 3702.7 925.675 28.36 0.000
treatment factor 3 34.8 11.600 0.36 0.786
Error 12 391.7 32.642
Total 19 4129.2

a)To check the difference in the treatment values,the computed F-value is 0.36

p-value=0.786>0.05,so we accept H₀ that there is no significant difference between treatment means.

b)To check the difference in the block values,the computed F-value is 28.36

p-value=0<0.05,so we reject H₀ that there is significant difference between different block means.