Please solve this problem with complete solution, step by step and use formula.
ID: 3183109 • Letter: P
Question
Please solve this problem with complete solution, step by step and use formula.
The U.S. Department of Housing and Urban Development provides data that show the fair market monthly rent for metropolitan areas. The following data show the fair market monthly rent ($) in 2005 for 1-bedroom, 2-bedroom, and 3-bedroom apartments for five metropolitan areas (The New York Times Almanac, 2006). At the 0.05 level of significance, test whether the mean fair market monthly rent is the same for each metropolitan area.Explanation / Answer
SS(total)=(each observation)2 – CM = SS(A)+SS(B)+SS(AB)+SSE
CM = (Sum of all observaions)2/a*b, where a is number of levels in the rows factor and b is number of levels in the columns factor
SS(A) = Ai2/b – CM, The Ai are the row sums.
SS(B) = Bi2/a – CM, The Bj are the column sums.
SSE = SS(total) – SS(A) – SS(B) – SS(AB)
CM = (1077+775+975+1107+1045+1266+929+1183+1313+1187+1513+1204+1725+1889+1537)2/(3*5)
= 23375041.67
SS(total) = 10772 + 7752 + 9752 + 11072 + 10452 + 12662 + 9292 + 11832 + 13132 + 11872 + 15132 + 12042 + 17252 + 18892 + 15372 – 23375041.67 = 1296935.33
SS(A) = [(1077+775+975+1107+1045)2 + (1266+929+1183+1313+1187)2 + (1513+1204+1725+1889+1537)2]/5 – 23375041.67= 874308.13
SS(B)=[(1077+1266+1513)2+(775+929+1204)2+(975+1183+1725)2+(1107+1313+1889)2+(1045+1187+1537)2]/3
- 23375041.67 = 350201.9967
SSE = 1296935.33 – 874308.13 – 350201.9967 = 72425.2033
dfA= 3 – 1 = 2
dfB = 5-1 = 4
dftotal = 15-1 = 14
dferror = dftotal - dfA - dfB = 14-4-2 = 8
MSA = SSA/dfA = 874308.13/2 = 437154.065
MSB = 350201.9967/4 = 87550.49918
MSerror = 72425.2033/8 = 9053.150413
FA = MSA/MSerror = 437154.065/9053.150413 = 48.29
FB = MSB/MSerror =
Two-way ANOVA: Rent versus Bedrooms, Area
Source DF SS MS F P
Bedrooms 2 874308 437154 48.29 0.000
Area 4 350202 87550 9.67 0.004
Error 8 72425 9053
Total 14 1296935
The p-value corresponding to Area is 0.004; because the p-value < = .05, there is a significant difference in the mean fair market monthly rent for the five metropolitan areas.