12.66 In order to provide its clients with comparative information on two large suburban residential communities, a realtor wants to know the average home value in each community. Eight homes are selected at random within each community and are appraised by the realtor. The appraisals are given in table below (in thousands of dollars). Can you conclude that the average home value is different in the two communities?

You have three ways of analyzing this problem

[parts

(a) through (c)].

a Use the two-sample t-statistic to test .
b Consider the regression model where Since testing is equivalent to testing Use the partial reproduction of the regression printout shown in Figure 12.37 to test . Use 0.05.
c Use ANOVA method to test Use 0.05.
d Using the results of the three tests in parts

(a) through (c), verify that the tests are equivalent (for this special case, ) for the completely randomized design in terms of the test-statistic value and rejection region. For the three methods used, what are the advantages and disadvantages (limitations) of using each method in analyzing results, for this type of experimental design?

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Community A B 43.5 73.5 49.5 62.0 38.0 47.5 66.5 36.5 57.5 44.5 32.0 56.0 67.5 68.0 71.5 63.5