QUESTION 8 (13 points) The data given below show the monthly market rent of 1 be

Question

QUESTION 8 (13 points) The data given below show the monthly market rent of 1 bedroom, 2 bedroom, 3 bedroom and 4 bedroom apartments for five metropolitan areas. 8 1100 780 980 1045 970 1365 930 1200 1200 1100 1520 1300 1800 1647 1500 1630 1450 1900 1800 1600 A researcher wanted to test whether there are any differences in true average rent in the different cities due to differences in the number of bedrooms. After analysing the data with SPSS, a researcher obtained the following output. Tests of Between-Subjects Effects Dependent Variable: Rent Type III Sum of Squares 1.945E6 3.596E 1622093.350 3 322922.8001 277859.450 33.454 3.596E7 4329.265 540697.783 65.100 9.720 Corrected Model Intercept Bedrooms Areas Error Total Corrected Total a. R Squared = .951 (Adjusted R Squared =923) 80730.700 001 99668.400 2 3.800E71 2 8305.700 2044684.550 a. Identify the experimental design used in this study. (1 point)

Explanation / Answer

a. There are groups of homogeneous experimental units-bedrooms (matched closely as possible) to compar ethe means of th epopulation associated with five treatments (five metropoliton areas). Thus, the study is randomizzed block design.

b. The complet emodel for randomized block design contains (p-1) dummy variables for treatments and (b-1) dummy variables for blocks. Therefore total number of terms in the model excluding beta0 is (p-1)+(b-1)=p+b-2.

complete model:

E(y)+beta0+beta1x1+beta2x2+beta3x3+beta4x4+beta5x5+beta6x6+beta7x7

Treatments (areas) Blocks (bed rooms)

c. The degrees of freedom were calculated correctly, the df(Total)=n-1=20-1=19

d. The p value corresponding to area is F=9.720 and p value is 0.001. The p value is less than alpha=0.05, therefore, reject null hypothesis and conclude that monthly market rent differs significantly for at least two areas.

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